I've taken the cover off, and noticed the battery seems to be leaking
slightly:

https://flic.kr/p/EdXFsh

There's a white furry deposit around what I assume to be the battery -
the blue thing centre top. The underside of the circuit board looks fine.

Is a replacement straightforward? I can solder after a fashion.

A recommended source for a replacement? A google search throws up quite
a few options.

Would I be best not using it until the replacement's in?

--
Cheers, Rob