A piezo can't be replaced directly for a switch as a piezo generates a voltage whereas a switch will drop the resistance between two points, but will not create any voltage.
Your current plans are to use that shop bought strobe? That will make triggering more difficult than using LEDs. A few modifications to the unit and it should be triggerable from an external source. Then, you just need to make a circuit to change the voltage spike produced by the piezo in the bass drum into a clean voltage change to trigger the strobe flash. If you can get the schematic of that strobe unit, it will help a great deal. If nothing else, you can just use the output stage and tube and install this circuit:
**broken link removed**