It might not be that easy actually, when the battery corrosion strips off the plating it can be quite difficult to solder a wire to it, especially if the contacts are made of steel or something instead of copper. When you combine that with the terminals being in plastic that melts easily it could end up being pretty frustrating for a beginner.
If you do end up replacing the wire, I would use a wire brush on a rotary tool to really clean it up nice before trying to solder it.