If you want to eat those squirrels, use a .22 LR... or take only headshots with your .17 HMR and plan on putting a bunch of gory headless squirrels in your game bag. I agree with an earlier poster: I only use standard velocity target-grade solids for squirrels and cottontails and take 'em sitting in the head.
If you are shooting these critters for pest control purposes, then the .17 HMR or Mach II are undoubtedly the better choices. Which one you pick depends on your average range. Under 100 yards, go with the cheaper (and slower) Mach II because your target won't know the difference. Over 100 yards, choose the HMR because you'll get more hits at longer range.
I see the .22 LR as remaining the King of Rimfire Hunting Cartridges (my choice for squirrels and rabbits), the Mach II as being the Ultimate 100 Yard Varmint Stomper (my choice for starlings, pigeons, turtles, etc.), the .22 WMR as the Reigning Rimfire Powerhouse (my choice for larger critters), and the HMR as the Ultimate Rimfire Varmint Popper (my choice for deflating crows, starlings, and ground squirrels out to 200 yards).
My rimfire fantasy: to find a tree row where the starlings roost and with a hill for a backstop, get 150 yards away on a calm evening, and shoot starlings with my HMR until it gets too dark to see.
Did I ever mention that I HATE starlings?