Is that a good option if a guy blows holes in hides with the wrong bullet? I would rather sell my hides, but I wonder what it would cost to tan and keep all of the ones I ruin?

Not that I think tanning hides costs that much, but it's sure gonna cost a lot to buy a new house every couple of years because I've completely wallpapered the house with ruined hides. It might be a huge deal for some of us who call in between at least a few dozen coyotes every season - not sure what a guy is going to do with that many for themselves...

For the OP: The 243win is only really suitable for 2 of the animals on your list - coyotes and groundhogs, and only barely so for either. It's going to be work (which is why you asked the question) to stop the 243win from tearing up hides. Nobody is collecting fur on groundhogs, and blowing them apart is kinda the point, but it's a bit much on recoil and ammo cost compared to a 223rem which would do that particular job just as well.

If you're using an over powered cartridge for coyotes - which the 243win IS overpowered for coyotes brought to the call - then a guy needs to use a stouter built, non-varmint bullet, and be sure to stay off of the shoulder. In other words - no tipped bullets of any brand or creed - they all expand too violently.

You're going to ruin more cats and fox than you don't with a 243win - I've yet to find a bullet which wouldn't mess one up pretty badly most of the time.

As you're considering your "varmint rifle" or "predator rifle," keep in mind the realities of the species you're hunting, because their differences in physical form and differences in how they are hunted are critical.

In most of the Midwest states, considering average sized adults, an adult Coyote will weigh roughly twice as much as an adult bobcat or raccoon, and 2-3 times more than a fox - you have groundhogs on your list, which are around a third to half the size of a fox... Itty bitty things. A coon and a bobcat of equal weight have VERY different body shapes/types, and respond to a bullet very differently.

Cats and raccoons will generally be best hunted in cover and fox are best called in cover or on edges, whereas coyotes are more easily hunted in open spaces, so shots on cats, coons, and fox on average will be a lot shorter than those for coyotes - couple that with their smaller bodies, and you're talking about a VERY different demand. I generally figure on shots between 75-300yrds for my coyote sets, but for most of my fox, coon, or cat sets, 25-75yrds typically.

For coon, I almost exclusively use a 22LR, pistol when treed over hounds or in traps, rifle when called. For called badger & coon, I typically use a 22LR rifle and target head shots, but will often employ 22WMR, 17HMR, or 17WSM - rarely but occasionally a 22 Hornet.

Cats and fox are really best hunted with 22mag, 17 HMR, 17WSM, 17 or 22 Hornet, 17 or 221FB, or up to 223rem. The super fast 17's and 20's can be messy as well on these, but but 17FB/MachIV, 204rug, or 20 practical are good qualifiers as well - especially when loaded down. It's just too easy to tear up hides on these smaller game species. I don't take headshots with these, as I do with badgers and coon, so I run a little more cartridge, in general.

In decades of doing it, and hundreds of predator hides sold, I can't say I really believe there's a bullet loaded in a factory round for the 243win which is actually good for fur hunting fox and cats - especially when you consider a cat is usually worth 10x what a coyote might bring.