New unit probably doesn't worth it. Because after you bought it, you'll still have to prime it, paint it then protect it with lacquer.
If you want to do a perfect job. It will be removed the mirror from the car, remove the peeling paint (or at least use body putty then sand), respray.
Mirror removal process is fairly easy. Window all the way down, remove the door's inner plastic panel, detach the window control connector. With the panel out of the way, disconnect the electrical connector for the mirror, then unscrew 3 x 10mm nut that holds the mirror to the door.