Aguila makes a very quiet .22 round. Something around 750 fps at muzzle. Sounds like an air gun, but close in deadly. I’d not use it on a fox, however, as I am, in the end, pro-fox.
A high power .22 pellet gun* will work on varmints up to 15 lbs. or so, but might be iffy on foxes unless you are a great shot.
*Mine air rifle is 1100 FPS, depending on the pellet, so that’s getting close to the speed of sound / noisier. But, the long barrel pistol is, IIRC, more like 750 fps: Very quiet, but I’m pretty sure lacking enough punch for a fox.
What about one of those mini crossbows?
“MY air rifle...” Sheesh!