I've called and shot a lot of coyotes over the years. My experience with the very light 243 bullets and high velocity has been just the opposite. When I lived in the lower 48 I skinned coyotes for several of my friends who called a lot of coyotes as well as handling my from trapping and calling. I got to see first hand what worked and what didn't. I've seen a number of coyotes that looked like they swallowed a hand grenade after being hit with a 55 grain 243 Ballistic Tip. I expect the results would be worse on the light and more fragile foxes and cats.
I'd go heavy (95-105 grains) and moderate velocity if your saving the hide for a mount. There's no guarantee that you won't get some foxes or cats with big exit wounds but the odds are in your favor. The bigger bullets just don't seem to tear them up so bad, especially if you can keep the shoulder out of the shot. You'll have an exit wound but it should be minimal, one inch or less. I think I'd also give the FMJ's a try. I really never had much success with them in 22 centerfires on coyotes but in a little larger caliber and on the lighter foxes and cats, they might work alright.
Mark makes a good point on the 22 magnum. Its a great round, along with it's little brother, the 17 HMR. Both will work on called in predators and pelt damage will be minimal to non-existent.
Good luck. Predator calling is a great thrill.
