Honestly an ideal application for wireless power transmission. The power usage of the device is low, and there is typically a substantial delay between uses, so

Honestly an ideal application for wireless power transmission. The power usage of the device is low, and there is typically a substantial delay between uses, so a very low power RF source could still be sufficient to keep an internal battery charged. Position is static so the RF source could be highly directional for improved efficiency. That being said, if you have an RF source, why not have it be the transmitter? Have a passive antenna in the switch that activates when the switch or sensor is active. The RF source detects the returned signal and then communicates with the powered device. Hell a clever engineer could probably get this to work with standard wifi.