That is tiny. Smaller than the mosfet driver - how small can they get.
Just a thought - how about a pressure sensitive resistor in place of the pushbutton. A bit smaller than the battery diameter and very thin, except for those long leads. It's less than the battery diameter and could sit outside the battery cover? Don't know? Maybe?
Finger pressure...
http://learn.adafruit.com/force-sens...r-fsr/overview
https://www.sparkfun.com/products/9375