In case this should prove useful for someone else - I needed a T20 screwdriver (at least 100mm long) and a T10 screwdriver. Remove the battery compartment sleeve and use the T20 screwdriver through the hole in the end of the battery carrier to undo the screw in the centre of the battery carrier base. Carefully lift the battery carrier off and you'll see two T10 screws (you can get to these without disconnecting the wires, just be careful). I undid one, then started undoing the other and the button popped out. Reassembly is the opposite of disassembly, as they say in Haynes manuals.
