Driver shown with the wiring removed.

Leave the existing wire the way it is guided through the shell. Just use a sharp knife and remove the outer insulation.

About an inch of insulation is removed, showing the two wires. Copper color is ground red is + on the driver. There is no visual insulation on those strands. It is not necessary to remove any insulation from the two wires themselves. The heat from the soldering iron will melt that insulation.