How to safely remove battery connector?

Hello guys,

I got an iPhone 4S in repair, it was already in repair in another shop but they just made it worse so I'm on it now.

It just needs a display assembly repair but the real problem is, when I opened it and removed the battery the battery connector came off the logic board (again.). With it one solder pad (the one next to the grounding). I scratched of an extreeeemely small piece of the trace and put a very small amount of solder on it and it actually works - for now.

But the display assembly is not there yet and I have to remove the battery again so my question is:

Is there a way to safely remove the battery without ripping off the battery connector?

or would you recommend (in this case) to leave the battery on the logic board and just remove everything except the battery to replace the display assembly?

I don't know what happens when I remove the battery and the solder comes off again, I don't want to risk ripping the trace off the logic board, that would be pretty expensive...

Thank you very much! :)