replacing disposable lithium-thionyl batteries with rechargable lithium batteries?
Few things to take into account when replacing the batteries, are the cells conneted in parallel (higher current) or in series (higher voltage)? Does your device have a regulator and reverse voltage protection? Shorting an LiSOCl will just make it warmer, shorting a LiPo cell might cause an explosion.

You said it is a wireless device, 2 1/2AA LiSOCl cells in parallel can provide a 200mA pulse, check if your intended replacement cell can provide it.

Self discharge: LiSOCl cells have low self discharge and very long shelf life. Rechargeable cells have much higher self discharge and if the cell drops below a certain threshold, it cannot be used anymore.