Hi Tom and welcom to Electronics Point
I think you would be better off joining a forum specifically about antique radios. Electronics Point is oriented towards general modern electronics subjects. We do have some more senior people here, but I don't think they're into antique radios. They will correct me if I'm wrong
The basic answer is, as Gryd3 said, if it had a non-polarised plug originally, then you should be able to wire a polarised plug either way around without causing a hazard. But there are usually ifs and buts, and it's best to ask people who are familiar with the make and model you're working with.