I've shot many coyotes in snares in the brain with a 22, and I'd say 80% of the time they usually take another. I have shot and killed 2 coyotes on the spot with a 22 while calling at nite (it is not legal to use anything bigger than 22lr when calling in SD after dark with a light). So, in my experience. I would say, yes, it will them, are there better choices, Yes.

The 17HMR is not a better choice. I've seen what it does to big coons, badgers, skunks, etc, it very rarely anchors them even with a well placed shot.