This thread may help:
viewtopic.php?f=58&t=6138&hilit=hamilton+battery
Unfortunately the images of the battery are missing. They talk about a little pin protruding from the battery, so I'm guessing it's the same. It seems it's 3V, and you'll have to muck around with a lithium cell and get creative with some conductive strips.
Let us know how you get on.
Rgds.