Last time my battery ballooned, I had to risk turning it on and wiping my hard drive first.
The reason is that I have been asked for my password before and they wouldn’t accept my MBP for service if I didn’t give it to them.
If they still need your password to repair your computer, they really need to update their procedures.
Back then I just winced, gave them my password, and crossed my fingers (seems to have worked out), but these days I just couldn't do that. There's all kinds of financial and identity stuff in there.
Sure enough, after a few days I get the laptop back to see the hard drive's been wiped, supposedly because there were errors with the OS installation, though there were none that I picked up actually using the device.
Not that it's possible with Apple devices anymore, but that taught me I should have just given them the laptop without the RAM or SSD installed at all.