No one can prevent you from singing words in the public domain to any tune in the public domain.   Their copyright in the words reaches to any additions or changes they made to the p.d. words, not to the p.d. words themselves. Their copyright in the music reaches to any additions or changes they made to the traditional tune, not to the traditional tune itself.

Of course if all you have is their version, it may be hard to separate out their copyrightable components from the uncopyrightable ones. I call this the "derivative work deconvolution problem."