That would be a fun project. I'd complete the strippage and just spray a thin coat of black nitro on the body, however I have enough precisions at the moment.
If you want to get it working and sounding fantastic without any soldering required, I can recommend the EMG Geezer Butler pickup which comes with all the the wiring, pots, socket etc and is so easy to install that it feels like cheating. — I have 'em in two of my precisions.