Yeah, that's a bit of dilemma. I faced the same one when my battery failed. The USPS will charge about $20 to send the camera back to China. Of course, that's uninsured, no tracking. A bit of a hail Mary. On the flip side, the battery is less than half that cost (which I bought), and the seller agreed to send me a new one at no charge.
These LiPO batteries are pretty stout. I've had some cameras go many years without ever having a battery fail. Still, it's a possibility. The effort and cost involved in changing one, I think, is minimal. A total of four screws, and a little bit of patience, and some minor soldering, and you're 100%. Certainly easier than shipping it back to China - IF that is your problem.
Everything I've read indicates that these cameras must have at least a minimally-charged battery attached for them to work reliably. I've not tried it without, but others have, and they say it must be there. I also remember someone posting a modification where they ran a lead out the case for an external battery. These are all reasonable hacks, but IMHO, unnecessary given the relative simplicity of replacing the battery, and the clean look of no additional wires.