Unplug the old base from the wall.
Turn the base upside down and remove the casing screws with the screwdriver. Pull the case apart and then locate where the wire end contacts are soldered inside the case.
Plug in the soldering iron. When it heats up, place the tip to the soldered wire contacts. As the solder heats up, suck it out with the solder sucker. Remove the wire with a pair of needle-nose pliers and then slip the old cord out through the base's grommet.
Strip the outer sheathing off of the replacement cord with wire strippers. Also strip the ends of the individual wires inside the cord back about 1/2 inch.
Slip the wire end through the grommet on the base.
Hold the solder to the contacts and solder the ends of the new wire into place. Allow the solder joints to cool for three minutes.
Place the cordless drill base casing back together, insert the retaining screws and tighten them with the screwdriver.
Plug the new battery base cord into the wall to test it.