The .22 Hornet isn't exactly loud to start with. The 35gr v-max is probably not the best choice for the job at hand, but since that is what you have, and LilGun is the powder you have, try loading loading below max for a velocity around 2800. This should be just over 10gr. Check reloading manual.
This will be a lot quieter than your .222 while still enough soot to cleanly kill a fox at your indicated ranges, with appropriate shot placement of course. Fast powder all burnt before the pill exits the muzzle is the key to low muzzle pressure and hence noise. This is not sub-sonic and you will still get the crack, but going sub-sonic with a 35 -45 gr pill is marginal on fox.
Contrary to popular belief, the v-max's work very well on thin skinned game if slowed down, and 2800 seems to be the sweet spot. Penetrate rather than splash.
To better help you it would be useful to know what powders and projectiles you have available to you.