I'd guess, even though your 7mm-08 is concidered too large for coyotes, that using the fail safe bullets will not do too much damage becasue they are a hard bullet, built for big game, meaning that they probably won't expand much on a coyote. After you shoot one, you will be able to verify that first hand. If the bullet doesn't hit shoulder bone, I bet the exit hole won't be too ugly. I've shot coyotes with my .300 Win., and the exit holes were smaller than what my 22-250 leaves alot of times.