For small game, squirrels especially, I use a pressure cooker. Cook until the meat falls off, or can be easily pulled off the bones. Watch out for the istsy-bitsy ribs (hate 'em) and then use in a spaghetti or mixed meat soup or stew.
Some folks LOVE squirrel. I'm not one, but won't shoot what I can't eat. So I eat the suckers.
For rabbits, often the same, tenderizes the meat, makes it easy to pull shot out, and, as you inquired, allows you to freeze the cooked meat until you have the occasion to use it for your meal.
Wild turkey? eh. Tough bird to hunt, tougher to eat. They, and wild geese, should be made into sausage. I think I've had two that were not so chewy it was an exercise program, not a meal. Even the pressure cooker doesn't help much.
Game birds...figure to freeze up to three months...you can bake a closed casserole meal with cream of mushroom soup (undiluted). Pheasant is what I've eaten most of; grouse is what I want...but very few around here.
Wild ducks...need some care. Best I've had is browned skin and then baked for an appropriate length of time. Season to taste. Can't speak for ocean fly-way birds, I usually just see woodies and mallards. Sometimes a teal, but for the return of meat-to-cost-of-shot, teal aren't worth it.
But the deal is...fat gives us most of the taste. Wild game has very little fat. Domestic fowl hang around and smoke dope all day. They are fatty. Wild game are training for the life olympics. They are lean.
Of course, YMMV. I'm a meat hunter, mostly. Pheasants are the only bird I hunt for sport, and most of that is to watch the dog work. The cost of getting the meat has to justify the return on that investment.
A two year-old doe is fine for my annual needs.
BUT...it does serve to remember that I have other options when I'm cooking game. Real hunger makes all foods very, very tasty.
Kis
enjoy every sandwich