Word to the wise here, you can easily get prion disease from eating squirrel brains (an epidemic brokeout in KY where it's more popular). Be sure to cook 'em well. You DO NOT want prion disease. It eats YOUR brain basically.
Haven't had squirrel or rabbit in a long while, but one thing I never forgot was DOVE! Dove meat is probably my favorite, period. And I almost never get to have it, especially here. We'd just twist the wings off at the shoulder, high on the shoulder, and stick a finger under the breast bone and just pull the breast out of the bird. Skin and feathers come off, you can prep one for the grill in a minute. Rinse in water, wrap in bacon --mmm, the best.