That would be my thinking but really you need to attack this all at once. It is a bit time consuming but it should take less than a day to go through the majority of the stuff and remove anything that is not factory and (I stress this) properly repair any of the factory wiring. Aviod using cheap crimp connectors when possible, the cheap ones have very thin and weak metal crimp tubes inside and are prone to fail, best is solder and adhesive heatshrink to repair wires but I realize that is not in many people's toolboxes.

 

^X2 Solder heat shrink connections! Main thing is to match the wires. There are solid colors and colors with tracers: