Is the battery soldered? Is it a fairly standard kind of thing like an 18650 (obviously not the same size, but I'm not familiar with what "standard" pouch style batteries exist)?
It’s not soldered, but it does have a Molex Pico-EZmate connector (chosen for its low profile), and I’m not sure you can find batteries premade with that kind of connector. You could reuse the existing connector with a new battery, but that would ideally involve soldering.