9 volt rechargeable Battery

Possibly not. Back in the day, 9V Nicads had six cells. This made them 7.2V nominal batteries. But most NiMH 9V batteries use seven cells for 8.4V nominal. Some even have 8 cells for 9.6V nominal. So a NiMH 9V could have too high a voltage for a device designed specifically around a Nicad 9V. However, a seven cell NiMH 9V will be fine for anything designed around an alkaline 9V.