<< What do you think might be the best weapon to hit a prey on distance for a survival situation if you are not permitted to own a handgun? >>

It seems to me that it depends on how large an animal and how far away. Also, how much weight and bulk are you willing to lug around? And... this is the really important part - how much disciplined practice will you undertake to make it worth your effort?

Because everything suggested so far and things that have not been suggested take skill to be good enough to rely on and skill can only come from practice. If you cannot afford the time to practice, your efforts and money would be better spent on the best emergency rations you can afford to purchase and carry - and then you must carry them, of course <grin>

I'm not knocking the idea, at all - just trying to point out that there's no trivial answer. I've had opportunities to forage/hunt/fish for food on outings since I was a child in environments as rich as here in the riverine areas of the upper Mississippi River Valley to as sparse as far North Alaska and in all seasons. Some of my trips have relied/attempted to rely on foraged food for various reasons and my experiences have been fun, educational, and given me some great stories to tell...

With that out of the way... you specifically mentioned handguns as "out" for you - fine; they require the most skill of all projectile weapons anyway. And you sort of ruled out other firearms for various reasons. IMHO, the reasoning you used against rifles and shotguns would apply equally to your crossbow, but if that's what you want to carry, have at it. I am NOT familiar with that EXACT model, but Barnetts are typically about 150 pound rated bows with a 20" to 22" bolt/arrow, so I guess they would be ok for up to medium game like deer, maybe larger game. I have no personal hunting experience with crossbows, so I'm just making an educated guess here. Crossbows are pretty maintenance intensive IMHO and they are HARD on projectiles when you miss the quarry and strike something less yielding, but I suppose you know that and can manage.

Perhaps this would be of interest to you: A modern self-bow made from synthetic materials could be integrated into a fixture that melds the bow into a walking stave (a REAL stave that is head-high on you, not a "treking pole"). Deal with arrows anyway you see fit. A 40 pound - 65 pound bow can be a fairly effective tool for small game to fairly large non-dangerous game if you are practiced with it. Like all hunting tools, practice needs to include realism, such as field-shooting with a bow - range estimation is extremely critical with low-velocity weapons like any sort of bow.

(Thanks to Chris K - this "walking bow" was sparked partially by his atlatl "hiking stick" idea. Hey Chris, I am very slightly aquainted with Bob Perkins and his atlatls are awesome - I suck with those, though - it's the "practice" thing - give me a firearm; any firearm... <grin>)

I could carry on, but since you pretty much rule out firearms of any sort... things like throwing sticks work OK and you can usually fashion those on-the-spot (The "apache throwing star" type is the easiest to use effectively IMO). Given your constraints, I think a plain old self bow is worth your consideration, especially if you can contrive to integrate it into a multi-purposed bit of gear.

HTH,

Tom