I did the same thing too!

You can use the "Blue" masking tape to insulate the new battery wires. Also you can use the "Blue" Masking tape to hold in the wires and the battery before soldering. Reason for the "Blue" tape is it's less sticky and leaves no residue.

Or you can use a "Solder Sucker" that has a plastic tip so it's less likely to short out.