Sourcing 3-lead 3.7v LiPo batteries
You say these things are medical devices.  The general answer is therefore that you shouldn't be in there messing with them.  You should only replace parts if they are intended to be user-replaceable.  In that case, the details would be in the manual.

Medical devices are governed by a large set of regulations.  The manufacturer had to perform lots of specific tests, keep very specific records of the design process, and get certification.  Here in the US, it is the FDA (Food and Drug Administration) that handles such certification.

If you do anything to the device that is not sanctioned by the manufacturer, then the device will no longer be certified.  You would be committing a federal offense if you then use the device on patients.

Most likely, nobody would ever notice.  However, if something happens and somebody gets hurt, even if ultimately not due to your mod of the device, you would be in very serious trouble.  The jury will hear all about how you were so irresponsible and had so little regard for patients that you performed your own highly technical jargon-laden unauthorized modification of a very sensitive medical device.  The final nail in the coffin will be when the plantiff's lawyer enters this Stack Exchange question into evidence, showing that you even knew you had no idea what you were doing.  Even if by some miracle you escape a serious judgement and somehow manage to keep your medical license, the FDA may decide to file criminal charges.

Or, you could avoid all that and have the manufacturer perform a authorized repair.  Sure, they might charge $150 for what will probably be just at $3 battery, but you get to keep your house, the privilidge to practice medicine, and you won't be public declared a dirtbag by a jury.