Sooz, most kazoos have a way to unscrew the bit that sticks up or out or whatever, so as to allow you to replace the paper when it gets blown out or worn or wet. If yours is that variety -- you'll be able to see the threads most likely if it is -- then just take the paper out and soak your lozenge out of the tube, or stick the whole shebang under the tap, let it dry, replace the tissue paper, and bob's your uncle, it will play again.
Blessings,
Barbara