You may want to use the Teensy (which is Arduino-ish), instead. It's designed to work as a USB device, and has a mouse examply you could hack.
The new Uno is said to have similar capabilities, but I don't know whether there are examples available for it yet.
The piezo you showed us looks pretty generic, except that (nearly??) all the ones I have are made with a hole in the brass disk so that almost all the piezo part is exposed. Probably because they were made for use as speakers. The solid brass disk might be necessary to keep sweat and oils from getting on the piezo disk. Or it may be coincidental. You should find out before buying more.