I agree with Nigel, there is unlikely to be any significant free space in the battery itself.
There is probably some spare space in the drill body though, and that means it is independent of what battery is in use.
For the simplest approach, just a basic bluetooth 4 module could work, using the "state" (connected) output to control a power switch of some sort.
eg.
**broken link removed**
That would enable it just by connecting with a utility such as BLE Terminal or Air terminal etc.
If you wanted a persistent or password-controlled switch, you would have to add a microcontroller, even something like an 8 pin PIC12 that could receive and interpret text commands sent from the terminal app.