I had that problem with my '50. I slid a short section of heat shrink tubing over the end of the horn wire up through the hole in the mast. I then applied some heat to the portion of the tubing which was outside of the mast to hold it in place. It worked like a champ.
I am guessing that the only part of the wire which was missing insulation was close to the hole in the mast.
It was worth a shot to try the heat shrink tubing fix. If that had not worked, I would have had to order a pricey new mast bearing which comes with a new wire, and pull the steering wheel and the old bearing. I do not know if the '39 has the same design for the mast bearing/horn wire.
Carl