Split Gamecube Controller Cord - Any way to replace it without soldering?

[Crenando]

My Gamecube controller, the one I train and play with in competition, recently had its wire split right at the base of the controller itself. Since it still works perfectly, I could just put electrical tape over it, but plan on having a guy I know turn this thing into a piece of art in a week or so (custom-painted front shell, transparent back shell, LEDs that pulse brighter with every rumble) and I would HATE to have all that ruined by an ugly chunk of tape over a cable.

I have a ton of other controllers and would be interested in simply replacing the cable itself. However, I don't have any soldering equipment. Is it possible to replace the controller's cable in some other fashion?