The Cadet was designed for .22 LR, although like any .22 LR gun, it can also fire shorts and longs as well. Because the sights are fixed, correcting a tendency to shoot high would have to involve adding metal to the front sight since (IIRC) cutting the rear notch deeper is not practical on that gun.
I would try some different brands of ammo before doing anything, though. You will be surprised at the differences.
Jim