I shot a pile of squirrels over the years. For a long time I used a bolt action Mossberg which I had foolishly taken in on a trade & then found the only way to get a return on my investment was to Shoot it out, no resale value at all. Even in my youth when I had good eyesight could never shoot open sights well, could do better with a peep.
On this gun I ended up mounting a 3x7 variable Bushnell 7/8" tube .22 scope. Kept it set at 5 power & never changed it. This rifle was a tack driver with LR ammo but shot about a Ľ choke pattern (50% in a 30" circle) with shorts. Thus my ammo pick for it over all the years I used it was Standard Velocity LR's. Only bushy tails I can recall lodging hit in a fork while falling on the way down. In that situation it would not really have mattered if they had been Killed with a Daisy Red rider or a .600 Jeffrey Nitro. They didn't hang on the limb they were shot on.
I never used High Velocity loads because of the Sonic Crack, most efficient method I ever found for clearing a tree where a group of squirrels were working. Give him a head shot with that Std Vel LR & let him lay where he falls, within about 2 mins the rest will be back to cutting. A high vel would normally clear the tree with the first shot.
Just my personal experience with the squirrel.