TFF!
I got a batteries where the wires broke off of because they were cold soldered. I peeled/cut the cover off at that end and resoldered them back on no problem, use a soldering iron about 50 watt max with a point on it, not a soldering gun just be careful working on that PC board you dont get solder on anything else or it will make a heck of a bang when it shorts out and lites up! If you dont have that large heat shrink to recover the end with use a few layers of electrical tape, It is not the preferred thing as the tape gets soft when it gets warm and my come off.