As others have alluded to, an environmentally appropriate carry is important.

I used to have a nice survival knife in my computer bag and then realized that it could easily be misunderstood in that context (it moved to my BOB). A leatherman-type tool with screwdriver functions can easily explained in my computer case even if it had a large blade.

An ex-coworker once drew me into a sexual harassment suit against the organization (I was a witness not the target of the suit). However, I did have to explain my gun collection in court documents. I don't carry, but I do hunt and have some relic and curio guns.

It was a cheap lawyer ploy, but just goes to show how things can be twisted. For that reason, I wouldn't suggest carrying oven cleaner unless you could prove you bought it that day and had a receipt. The same goes for any OTC product which a "reasonable" person would think is inappropriate. For example, if you carried a household hammer into the DMV while complaining about your license, you would definitely get an LE intervention despite the fact that almost every owns a hammer - even if you didn't explicitly threaten anyone and it was just on your person.

The self-defense umbrella is a good non-threatening alternative. However, if some incident evolved into its actual use. You can be sure that the fact that it was not a normal umbrella would easily be brought up in a court case.

In a non-urban environment, there are definitely more choices. Be prepared, but don't be stupid.

There was a local court case where some teenagers got into an argument at a party. One guy went to his car and came back with a snow shovel swinging it around and threatening people at the party. Some kid got his nose broken. Although the guy with the shovel didn't hit anyone, his actions and the injury nabbed him a felony. As far as the jury was concerned, his actions contributed to someone being hurt - even though he didn't actually do it. Be smart and don't rely on the interpretation of any particular law to protect you.