Placing the button as in the original project would make it awkward to use the thumbwheel, so I opted to put it in the top right as shown here.

New button location carved out. There was a small trap door here which was removed to give better access.

Battery positive trace cut and wires routed to the new switch.

Switch installed and PCB replaced. There was no need to cut the PCB as the switch just squeezed underneath.

All back together and working fine. I found super glue wicked up into the switch and stopped it working so instead I just wedged the switch in place with the little trap door.