Here is a chart that gives some interesting numbers.
.22lr velocity loss and real world weapons
I do not claim this is precisely accurate: but may be useful from a comparative point of view. Lot variables from producers have to be factored in, as does all aspects of maintenance of firearm and shooting conditions.
What I get from this is that most high velocity ammo [1180-1280fps] is not supersonic in a 'normal' pistol, as it isn't above the 1127 previously mentioned.
HYPER-Velocity [Stinger, Yellow Jacket, etc] ammo [above 1300fps] is generally frowned upon in a semi-auto handgun, but would obviously be above that supersonic threshold.
Thus, it appears you are not hearing a 'supersonic crack' to begin with. It is just the report of the ammo.
If you shoot at an indoor range, find an outdoor one. the sound will not bounce around the interior to disturb you.
If you are truly this sensitive to the sound but enjoy target shooting/plinking: I have two suggestions for you. These are based on the assumption that the sound and muzzle flash are truly this disturbing for you. I am not judging, but working to find a solution.
1st possible solution: get a .25acp handgun and handload. .25acp has a FPS of around 800 and a FT/LB of around 60: or about 2/3rds the power of a standard or high velocity .22lr. It would be a semi-auto handgun that is designed to cycle properly at the power threshold of .22 longs or .22lr sub-sonic ammo.
Handloading would allow you to find powder combos that avoid the muzzle flash that you identify as disturbing you.
Advantage: you would be able to continue firing a firearm while reducing the sound and muzzle flash.
Disadvantage: a new gun and reloading parts would be needed.
Second solution: have you thought of an airgun?
You can get all sorts of cool bb pistols and pellet pistols that shoot between 300-500 fps of round, using CO2 to drive it. A quick search of PyramidAir showed Makarov/1911/Beretta/Witness/S&W Magnum and a variety of other types. Some even have 18 shot magazines.
I am not joking.
It seems like you are unlikely to find what you want in a semi-auto .22lr handgun.
These two options
would help address your concerns, while continuing to plink or target shoot.