Snares and baits are two items which are very handy when hunting small and timid animals. If you discover traces of, for example, a rabbit, equip snares, place them where the animal was before and throw some bait onto them. You can hide in the nearby bushes and watch the animal or head completely elsewhere and return afterwards.
Skinning hunted animals is trivially easy. Just approach a dead animal and press the interaction button and Connor will automatically cut out everything that's of any use.