I need to replace one of the red power wires that leads to the bulb because the connector has broken. Can I just unplug it and and replace just that part?
Buy the assembly. These wires, especially near the lamp, get very hot and will oxidize and make a poor connection....oxide is usually an insulator, thou copper oxide is a semiconductor. The wires are very well connected to the connector. You'd have trouble doing as well.
Now that you've busted it, replace it. It'll be cheaper in the long run.