The controller is a fairly universal one. Mercury Electric made about 700 gazillion of them. They don't usually go bad unless mistreated. The cord is connected inside by two screws. No reason to replace that unless it's actually bad.
The cord plug is another matter. I've not seen one like that. If the plug cannot be opened to replace the wires I don't know where to find one.
From your pics the wires do not look to be all that bad. I don't see any cracks or missing insulation anywhere.
Does that plug have a screw crosswise through it or some other means of opening it up?
Joe