Couple more thoughts...
Spot-and-stalk hunting means you "move differently" than when you're just hiking along. You move a lot slower, you stop and listen a lot more.
You'd want to take a very lightweight .22 with "short" hollowpoint rounds. Take only the ammo you need (eg, you don't need a whole brick of 50.) Depending on how long you're out, you may want a small cleaning kit, at least for the barrel. You'll want something that "breaks down" so its easier to carry - something like the Ruger 10/22 or the Marlin Papoose. Another option is a small .22 pistol or airgun (.177 or .22) that you can pump up. Smaller, lighter, lighter ammo, quieter. You'll have to get closer, so make your call wisely. Skip scopes; too much maintenance and you shoudn't be taking long shots anyways, especially with the .22-shorts. Iron sights work fine and they won't get knocked around at all.
Using a whistle or predator call will cause many animals to "freeze."
Be sure you have license, season regs and you know your zone boundaries.
Some places allow you to shoot fish, but watch your angle because, like a rock, you can "skip" a bullet. Better to just take a few feet of line, a couple small hooks and just use grasshoppers and worms. (Did this with the girls recently, they had a more fun with the improv gear than with their real poles. Bonus points for the fun of an hour out catching grasshoppers, too.)
Take notes and a small laminated card of edible bugs. You can spit-roast or flat-rock-roast them next to the fire.
You can eat snakes. They're pretty tasty and have quite a bit of meat. Make sure you know how to field-dress them, especially the poisonous ones where you want to cut the head off and bury it (the head) because it'll stay 'active' and move for hours after it's dead.
Practice beforehand. If you cannot get out there with real arms, go out and get close enough you think you could hit it with a thrown rock. Don't actually do it, but get close enough you can. Squirrels are easier than rabbits. Much easier. You have to hunch over and go really really slow, patiently, to get close enough to a rabbit. :)
As mentioned previously, don't shoot anything big. You want small things you can skin with a swiss-army knife and stick on a spit (or pan-fry if you're carrying a pan. Take a little oil, too, because wild-game is much less fatty than farm-raised. Not all game has enough natural fat.)
Take a pair of thin gloves, like a doctor uses. Watch for latex allergies. They'll keep your hands clean and help with fleas/mites/ticks/pathogens in the animal. Skinning and cooking will be required. Make sure your gloves are textured, and you knife is sharp ... preferably with a finger-guard-tang. Fluids can make knife handles slippery. Not required but they're stupid-lightweight so why not. Besides, multi-use for carrying water, cutting them up for making pressure dressings, and putting on your head to look like a chicken.
On your next hike, split your food. For every "animal you bag" by getting close enough, you're allowed to take one thing out of the "goodie bag." Challenge your friends, too, because then you get bragging rights (and memories) as well. Learn from watching them. Watch the animals and how they act/react.