Given that the user will typically have their watch on them as well, why not make the ring a battery-less BLE transmitter that triggers voice input on the watch? It’s still one-handed operation, but now the battery life is infinite since there’s no battery? The disposable ring seems like a solution in search of a problem to me, unfortunately.
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.
Example button: https://core-electronics.com.au/self-powered-wireless-switch...
I imagine the reason is reliability, but USD$99 plus international shipping every two years isn’t worth that to me, sorry.
Aside: I loved my kickstarter pebble and my steel, btw!