[svl7]

That could be achievable without a battery, using a Piezo button like some Hue remotes... Though not sure with the small form factor.

[lopis]

That's interesting. A Piezo Button generates enough power to send a radio signal?

[PMunch]

Indeed, I have a remote doorbell where the outer button is a piezo button and the inside bell part is connected to a socket. But the button is quite thick, presumably because it needs a bit of travel to get enough energy. Granted that's for a device that sends multi-wall penetrating strength of 433Mhz radio waves. For something like this where the distance is only about 25cm you might be able to get a button small enough.

[shellfishgene]

Have a look at the EnOcean kinetic smart home switches, there are now also other companies making them.