I hunt rabbits about 20 miles from you with SK Standard plus. They are an excellent accurate round out of my 22s.
Do you have any issues with the first shot going astray?
CZ rifle?
Cold bore flyers don't affect all or even most CZ's. If they do occur, they certainly wouldn't cause a miss on a grouse head unless shooting at distances approaching 50 yards on account of the flyer being just off a one-hole group. There should be no question about whether standard velocity .22LR ammo has the energy to kill a bird at hunting distances.