Hopefully, there won't be any broken strands on the inner cables. There weren't on mine. I just hung them upright and let oil work it's way down into the housing and all was fine. But, if they need replacing I think this bike deserves the full bore restoration treatment. These old cables have steel or brass ends that can be removed with a torch. The pear end can be salvaged and reused. New brake cables have the correct barrel end, so all you need to do is measure it out and silver solder the pear end on the new inner cable. An important thing...regular soldering flux for 60/40 won't work on silver solder. You must use the correct paste flux. Another trick...apply the flux heavily so the cable won't blacken from the heat.
If you need new ends, this guy has them.
Cable Parts « Myrons Mopeds