Can you replace the battery without soldering?
Is there room in the iPhone to simply cut the old wires, strip the end, and then attach the leads to the replacement battery wires? (of course using some heat shrink tubing to insulate the connections.) It shouldn't take up that much extra space, if you judge the lengths correctly. Judging by the photos here, I think there should be enough room.
I read so much about the difficulties of desoldering and soldering on the iPhone board, thought this might be a safer route. Of course, you still need to be careful not to cause a short, etc.