I think what you may find is that you have a pretty tall order to fill, especially for cats. I too have been searching for just the right caliber and load that will give clean kills on coyotes, yet not destroy a fox pelt.
Currently I'm using a .17 Remington and 25 gr. Hornady hollow points at 3921 fps. It drops coyotes where they stand, like they were pole-axed, but is too much for fox, at least with the bullets and velocity I have been using. Bobcats are fairly thin-skinned too, though maybe not quite as much as fox, and while I haven't taken a cat with the 17 Rem, I suspect results may be similar. The bullet doesn't exit coyotes, however.
I have been told that a .17 caliber traveling around 3500 fps is pretty good on fox. That load is near the 17 Hornet velocity. Not sure how it might work for coyotes though.
As to the .204, I have never owned one but I have read a lot of reports about it. To my understanding, the .204 can be tough on fur. I'm sure someone with more experience with that caliber will chime in soon enough.
Good luck with your final choice, and be sure to keep us all posted how it goes in the field.