Recently I selected three sets of mirrors, one set with intact mounting arms and the others with cracked plastic sheathing. My solution is to remove the sheathing, sand and repaint. The actual arm beneath the sheathing is some sort of hard, solid plastic material, which is easily smoothed, primed and painted.
I begin by using the Dremel with a cut-off disc to carefully cut the sheathing into smaller pieces, followed by cracking the plastic bits away with a screwdriver and pliers.
(click on an image below to enlarge)
(click on an image below to enlarge)
(click on an image below to enlarge)
(click on an image below to enlarge)