The .22 Hornet will be perfect for this. Mine's a very short barrel 13" or so with a JetZ CQB still pushing the 35 Grain V-Max at 3,000 FPS. It's not any noisier than the .17 HMR. If I can't be bothered to reload, then the Remington 35 Grain AccuTip are a good enough substitute.
Using the 35 Grain, I would suggest avoiding the shoulder, especially on a fox quartering into you. Head, neck or just behind the shoulder bones (if side on) works perfectly. Don't try and pin with it.
I'm happy to use mine out to 200 yards, but LRF and knowing the trajectory is very important, and that's a hard 200 yard limit. Most shots are 60-120 though.
Foxes I've taken with it (and it's an awful lot over the years) look like they have died in their sleep.
Cheers
Clive