I dont think leaving in the bullet will cause any problems, only if you swallow it might it be a problem. It was considered nothing to be eating any of the above mentioned animals, and spitting out a pellet or two onto the plate. Where I am from in Rome, it is considered standard on a menu to include both rabbit and pigeon. Most people would find this gross, but its what I grew up on.
I do agree with Evil1, in that these meats are quite tasty and healthy as well. Since all of them are very active animals, you wont find much fat on them at all. For this reason, you might want to cook them on a low to medium heat to not burn or dry them out.