Teaching yourself wheelbuilding is a great idea. You should do it
Helicomatic is not a great system.
See Sheldon Brown's article on it.
So the hub is broken? Why not rebuild the wheel with a freehub? That would modernize things nicely. Spread the frame to 130 or 135 and bob's your uncle, you have a modern machine, impervious to axle breakage and relatively future-proof. Shifting will improve too, with a hyperglide cassette. You can even find 126 spaced freehubs for hyperglide, if you look hard enough. You can take
7 of 8-speeds or 8 of 9-speeds and put them on there, to get a nice modern drivetrain with 126 spacing.
If you REALLY want to go ahead with Helicomatic, I think I have a couple hub shells and a cone or two I can send you if you make me a shipping label. Don't spend real money on that stuff!