[cwmoser]

I would not remove the winding.
Those wires are fine and fragile.
I would think it needs a coating if the wires are showing - but you cannot use just anything. Perhaps some other folks can advise.

Before going to the trouble to recoat the Flyback, do check for continuity. If a winding is open, that needs to be inspected to see if it can be repaired. There are some folks who have repaired windings but usually its when the open is near the surface.

First step is like you mentioned -- check for continuity on all windings. See if the Flyback as numbers or letters for each wired connection and compare that with the Schematic.

Carl