I'll try to dig up some suggestions when we get closer to release.
There are probably dozens of options as these are pretty common. 3.7v LIPO., rechargeable.
Something like this (as long as it's within the size range 25mmX5mmX37mm) :
5 x 3.7V 200mAh Lipo Rechargeable Battery 502025 For MP3 headphone smart watch | eBay
NOTE: The one linked does NOT have the little white connector for the power booster. There are batteries that DO have the connector so I'll see what I can find.
The one we used is 25mmX5mmX37mm. (I can see if it has a specific model number.) I suspect you might get away with something slightly larger, but I don't know- you don't want it TOO cramped inside. Since we got our battery locally here in 'little tiny Sweden', I reckon it will be MUCH easier to find elsewhere because our local selections are always lacking.