well, a classic bit with the American clowns has always been the alarm cloc wrist watch. Like this:
The back of the clock is removed by means of usually three screws on the back, and removing the stems and keys from the back. from there, you can attach an elastic band and fasten it to the case for a wrist stranp.
Good Luck, and a really Great Costume!
Cheers,
Scruffy