Wireless doorbell systems that have a kinetic-powered button (i.e. no battery) exist, e.g. https://www.amazon.com/gp/product/B0929729L1
Wireless relay receivers also exist, e.g. https://www.amazon.com/gp/product/B0B125VLNB
These products often use the 433 MHz band. Are there any that actually work together? What I really want is a kinetic-powered doorbell button that triggers a relay instead of a chime box.
What about a kinetic light switch instead of a doorbell? They work with mains electricity rather than a relay, but it might be closer to your needs. If you fiddle around enough, you could find a self-compatible set of doorbell and switch where you could pair a doorbell button to a light switch unit.
Or you could use the light switch button (some are ip65, apparently) and draw a doorbell symbol on it. Some industrial units I’ve been to have a massive button as a doorbell at the gates.
The problem with light switches is that they are latched relays that typically only output line voltage, whereas I need a momentary relay that passes through 16V AC from the doorbell transformer. Do you know if some way to adapt this to my needs?