You shouldn't have any trouble firing .22 BB or CB caps, shorts, or longs in a .22 LR handgun, provided you single-load them. On some weapons, you may even be able to use a lightened recoil spring to get shorts to function, the action, but I doubt that they would fit well enough in the magazine to function reliably.
Be aware, though, that extended use of shorter rounds will cause chambers to foul, and possibly even erode. When you use the shorter rounds, keep the chambers squeeky clean.