Piezo switches like the one you linked have a minimum size to generate the power necessary, and that minimum size is larger than the entire current ring.

The power generation portion of that switch is around 1.4x1.4cm and can power the transmitter to send a signal over 40m. I think it’s likely that it could be adapted into a ring form.

See: https://core-electronics.com.au/attachments/uploads/TEL0173-...