Installing a three wire cord is easy, just wire the hot and neutral to the same old points and ground to chassis. The two wire plug was not polarized, so don't look for some pattern.
I don't care what color wires THEY used. It isn't about color, it is about function. This simple circuit has the incoming mains wired to the fuse then power switch and on to the transformer. Your incoming hot goes to the fuse, the incoming neutral goes to the other connection.