Can you consistently hit the kill zone at 175yard.? If so good shooting. It wouldn't be a issue here because hunting with a handgun is illegal.
There is also a minimum caliber and muzzle energy allowed for hunting deer.
For all deer of any species - a minimum calibre of .236 inches, a minimum bullet weight of 100 grains and minimum muzzle energy of 1,700 foot pounds is the legal requirement.
Advice given by the BASC - The British Association for Shooting and Conservation
Although deer are comparatively large animals, the vital areas for clean kills are small. No one should consider stalking unless they can consistently shoot a group of three shots within a 10cm target at 100m.