BTW, you might want to know before you open the case that the battery you are replacing is labeled "ML1220/2E2E0X"
Another option is un-solder the original, find a generic ML1220 battery, and then solder the old pigtail connector to it, using shrink-wrap tubing to seal things back up.
[This battery is probably identical to the very common CR1220, both being 3V lithium button batteries. Dunno. Switch to a different model if you don't mind the uncertainty and risk.]