"I have always assumed that I don't need to worry about copyrights if I sing a traditional song......"

I don't think that's strictly true. It is possible to copyright a specific arrangement of a traditional song.

So for example if you were to sing "The Spinners" version of "Swansea Town" then they could theoretically get you for infringement of copyright.

I really don't think it's much of a problem unless you are (or some one is) making big bucks from the performance of a song.

Then I guess that you would ask the holder of the copyright.

Bert (always willing to pontificate on a subject - However little I know about it)