Hey, I am late to this thread, I have been out-of-town.

Very interesting discussion.

Will your trip be only in the US or are you traveling to other countries?

Mike

You might consider getting a CCW permit, and then doing your walking without your gun (I think it would be very difficult to research all the local laws that might affect carry given that you're walking and have less control over what property you might cross).

I think it would put a cop at ease to hear, "Hello officer, I want to let you know that I have a CCW permit, but I am unarmed." This should let the police know that you're a good guy, because bad guys don't go through the trouble and expense of going through an FBI and state police background check on their own. Note: CCW permits are for firearms, they do NOT apply to knives (at least not here in Colorado).

Already have my concealed weapons permit for SC, all set with it- Have an FOP card on the way too possibly.

I'm not a cop, but I have acquired some wits over the years. Much or all of this might already be common sense to you.
I have done some walking myself. Once while walking across Arizona along the interstate at night, a highway patrolman stopped and ask me all sorts of questions including if I had any weapons on me. I showed him that I had my Bowie knife and my belt slung over my shoulder concealed under my jacket. He told me this was illegal. I honestly didn't know. I put it on my waist without any argument whatsoever, where it was in plain view, and he was happy. Always be polite and respectful of officers. They don't know who you are, and they wan't to spend as little time sweating the small stuff as you do. The nicer and more appreciative of their presence you are, the more helpful they will be.
As I was in the desert many miles away from any town, he was concerned whether I had enough water to get me through the next day. He filled my canteen and left, wishing me good luck or happy journeys or something like that.
Another thing, lockback folders are illegal in CA if they can be opened with a flick of the wrist. Weapons violations in CA are usually felonies, including double edged blades. If you have one of those loose lockbacks, you might want to tighten it so it requires two hands to open.
The greatest threat to you, or anyone out on his/her own, IMO, is from other people who might want to take advantage of you. Pranksters, thieves, rapists, kidnappers, and murderers are all out there. Be aware of everything going on around you, especially the people. It is generally thought that wanderers are either naive (just finding themselves...) or dangerous (on the run or looking to...). I try not to let people get either opinion of me, but I think I'd rather be thought of as respectable for no reason in particular other than that I don't appear or come across as naive or disrespectful. If I'm not looking or acting like I want my time wasted, I usually don't get messed with. Prolonged eye contact with strangers can be bad. A smile sometimes goes a long way, but then again, don't look naive or suggestive.
Be wary of who wants to help you, especially when you aren't in obvious trouble, and always be prepared to defend yourself. Make sure escape is always an option. If you accept rides, I'll only say that trusting people can be dangerous. Always keep a watch on people's hands, and listen carefully to the things people tell you. Don't be distracted by their eyes, and don't believe everything you hear. Be polite whenever possible and assertive whenever necessary. Take a reliable pepperspray, and don't feel it's sissy to keep it equipped on your belt within easy quick reach or in your jacket hand pocket. Self-defense laws can be tricky, so play it safe by using non-lethal methods. Remember that if you have to use your spray, to follow up by alerting the authorities. Have a cell phone. You want the bad guy to get arrested, and by the time he gets released to take revenge on you, you have already changed your shirt and are long gone.
Most importantly, I think, is to be careful of where you sleep. This is obviously when you are most vulnerable. If you can't find a campground or motel, light day-napping in a friendly populated place is safer than where you can be followed into isolation or stumbled upon in the night by no-gooders. If you sleep in a sleeping bag, be especially careful where you sleep, as they can be difficult to get out of in a hurry.
Also, keep some kind of itinerary, and check in with someone you trust every now and then, like every few days, but no longer than a week.
I know I sound a bit paranoid, and I hope I haven't detered you from your goals, but I seen some s#!t, so I don't mind rambling a little. I wouldn't be able to think of myself as friendly if I didn't. Happy Journeys!

I am a Missouri State Trooper. If you are contacted by an officer be polite and answer any questions honestly. Lay down your hiking staff and keep your hands empty and in plain sight. Make any movements slowly and only when directed to do so. If the officer decides to conduct a pat search, comply with his instructions. Yes, you can be searched by an officer of the opposite gender. Tell the officer if you are carrying a knife, pepper spray or anything that could be taken for a weapon. If you have to reach into a pocket that contains a knife or pepper spray, tell the officer it is there. We don't like surprises. Explain why you are hiking. You will most likely be asked for identification. A computer check to ensure that you do not have a warrant for your arrest will be conducted. Plan your overnight stops to be off the highway. We dislike having a report of a "man down" and finding out it is someone sleeping on the side of the road with out the good sense to be out of sight. Being clean and neat in personal appearence counts a lot towards creditability. Having good camping equipment adds to the overall appearence. DO NOT carry a knife that gives the primary appearance as a weapon. Bayonets are not a valid camping tool, they are designed to be a weapon. No "Rambo" knives, just something that looks like a camping tool. Your pack can be searched because it IS on your person. If you truly support the FOP that is a fine thing. Just carrying the card to quote "get in good with us" smacks of being phony. Things that appear phony cause further investigation. Don't BS, tell the truth. Different jurisdictions have different laws relating to weapons. Generally laws are more stringent in cities than in rural locations. If you are told you have violated a law, apoligize and inquire how to be in compliance, then do so. Be friendly and non threating to the officer. Hope this helps. Have a great journey seeing our wonderful country.

The "Officer safety search" is based on the Terry vs. Ohio doctrine. An officer can "frisk" you (a brief, cursory patdown) for weapons while he conducts a brief interview with you. This INCLUDES your backpack because it is within your immediate reach. Courtroom legalities can always be argued, of course, but officers make good-faith decisions everyday that span both sides of the blurry lines of legalese. During the frisk, an officer is looking for anything that could be a weapon which, of course, includes knives.

Concealing a knife is ok if you meant keeping it in your backpack. That's simply carrying it as opposed to concealing. It takes on a different meaning if you're concealing it on your person. In New Mexico, a person can carry a knife or gun in plain view - it becomes illegal when it's concealed. Many States have similar laws and I don;t know them all but concealing a weapon on your person is almost always illegal.

As far as being searched (frisked), I would think it's generally not going to happen (note use of the word "generally"). Most seasoned officers can size you up pretty quickly and a quick wants/warrants and criminal history check, coupled with your truthful story of just "hiking across the country" will be more than enough. Keep your hands in his sight at all times and, when asked for ID, be deliberate. If your ID is in your backpack, for example, let the officer know where it is before you go digging for it.

DON'T immediately say you have a knife or weapon here or there, just answer the officers questions. Without a doubt, you'll be asked if you have any weapons or contraband. THEN you can say you have a knife here or there.

I don;t see a problem. Police are regular people, which means you'll get treated differently not necessarily by location, but by individual personality. Some are more aggressive and assertive, others more relaxed and congenial. Some are new and others experienced - some are wise and others not so wise. ALL of them, while dealing with you, will be watching every move your eyes and body makes, and listening to how you respond to questions. As I said, experienced officers will know intuitively "who" you are in a very short time, the same way a dog seems to sense danger or ill-intent from a person.

In my opinion, everybody seemed to have some good advice, but OBG's, Susan's, and Trooper366's posts especially caught my attention.

There are alot of good, well-intentioned people walking or bicycling across the country and police officers know this. I think you'll be fine.

Trooper gave some excellent real world advice but...

If I'm on the jury, the contents of the backpack is NOT admissable because getting inside the pack is no more accessible than getting into the trunk of the car and pulling everything in there out and putting it on the ground including dumping the toolbox out.

Accessible stuff on the outside- yes. Stuff on the inside nope. This juror calls BS on it.

Heck, I've been unable to find a couple of items that I was sure were in my pack. Could only find them after the pack was completely unloaded at home or in camp.

But I don't get to make the law and usually am dismissed from the jury pool for suggesting I get to judge the law. (Fully Informed Jury)

Being friendly and open will preclude having one of these experiences.

Just one question... what is a FOP card?

"...what is a FOP card..."

It is more of an east coast thing, Fraternal Order of Police, or something close...

You are correct... Fraternal Order of Police. As opposed to a PBA - Patrolmen's Benevolent Association. Both are organizations of police officers with FOP being the larger organization.

If you carry one of the cards, it shows that you support the police force, either you are an immediate friend or family of an officer. Often, out of courtesy, a policer officer may show leniancy.