I've seen small grey foxes tote .17 HMR bullets away. Also seen them tote .22 Mg bullets off too. It will kill them... just usually not dead on the spot. I'd take the .22 Mag in spades over the .17 for what you are wanting to accomplish. Just get ready to track the thing for a while. This is the one situation where I might well conceed to a shotgun as better for varmint hunting... or you could just do what everyone else does and shoot a centerfire anyway... law be damned.