Whatever you decide, don't leave them in the woods. If you do that, then you have no business being out there in the first place. Find someone that will take them, and do it before you go out hunting.
I have some family members that will eat deer and turkey, but won't eat squirrel or rabbit (they are non-hunters). So I will boil the squirrel/rabbit until it is done, peel the meat off the bone, then make a big batch of pork BBQ and toss the squirrel/rabbit meat in. They never know the difference.

--Man who fish in other man's well often catch crabs--