I suppose the traditional way was slow roasted on a little spit over the camp fire - or a long spit with several on. Or opened out, rubbed with herbs and cooked more quickly as with a fish. I would imagine those methods would dry them out though.
If I had to choose, I would fancy the slow cooked stew, with rich gravy and lots of herbs and tasty vegetables
I've never tried hedgehog, I hate pheasant, I love rabbit but I'm just not sure about squirrel....

.....ok, I would give it a go
As for coypu - well, they've eradicated them in Norfolk as far as I know, and I never tried one when I lived there, but I think that would be Occupation food ie when there's not a lot else.
Let us know how it tastes Dicky