Headshots with a .22LR is an ammo selection issue, not typically a rifle issue. Even a Ruger 10/22 or Marlin 60 will be able to do what you are asking in the field. The difference between the CZ, Savage, Marlin, or Ruger in precision will not make any difference at all for headshooting squirrels out to 125yrds. With good ammo and a bench, all of them will succeed, with junk ammo and off hand, none will.

Squirrels don't have big heads, you're talking about a 2" target, which isn't much margin for error when you consider even a 1moa rifle and ammo, then shoot it in the field instead of a bench. Asking for a "Maximum Point Blank Range" of 125yrds from a 1200-2000fps cartridge on a 2" target, for field shooting, just isn't realistic.

That said, you will NOT be able to hold dead on for headshots on a squirrel from zero to 125 yards with a .17HM2 or 22LR. With a 100yard zero in the 17HM2, you'll be an inch high at 60yrds, and 1.8inches low at 125yrds. With an 80yard zero, you'll be an inch low at 100, and 3" low at 125yrds. They just don't have a flat enough trajectory to reach that far with such a small target. You will have to learn to hold over (and under) to make it to 125yrds. Of course, doing so is not difficult - I personally zero at 100yrds, hold the crosshairs sitting at the chin/jaw from 50-75yrds, dead on at 0-50, 75-105, top of the head at 110, inch above the head at 125. If you limit your shots to 100yrds, then an 80yrd zero works, then from 90-100, just hold at the top of the head.

A 22LR only has a Max Point Blank Range - meaning hold dead on and hit target - of about 75yrds for a 2" target, which corresponds to a 65yrd zero. You will HAVE to hold over with a 22LR to get past 75yrds if you're headshooting squirrel, and for it I would zero at 50, then learn to hold for every 10yrds from 70 on out. And of course, you're going to have to shoot premium ammo only, as you're NOT going to get bulk junk ammo to group small enough to make headshots at 125yrds, even if you do know your trajectory.

A .17HMR zeroed at 110yrds will give you a flat enough trajectory to make headshots on squirrels out to about 130-135yrds, but again, you'll be lucky to deliver that kind of precision in the field (2" groups at 130yrds with a rim fire, NOT fired from a bench). The HMR is pretty close to over powered for squirrel, but if you're shooting that far, you'll need that much horsepower to get there.

So if you're dead set on 125 yard headshots and don't want to fuss with trajectory management, then a 17HMR or 17WSM are your only realistic options. Personally, I'd get a 22LR and limit my range, or get a 17HMR and deal with the excessive damage, in that order.