I don't know a lot, but I'd be looking at a .223. You may know more about furs than I, but a trapper I know, told me (about 1 1/2 years ago) that he has been unable to sell furs with any bullet holes in them period. Trapped furs only. I don't know your purpose, but I'd make sure I was able to get rid of them before I concerned myself about damage!
You shall know the truth and the truth shall make you free.--Gospel of John 8:32