With certainty, it was done by the Kingston Trio Copyright date is 1958. It is on their Capitol album "The Best of the Kingston Trio", Capitol ST 1705 released on April 30, 1962. It was also recorded by Tom Lehrer on his "That Was the Year that Was" LP.

I wonder if Sheldon Harnick expected the song to continue it's relevance. The song would imply that I believe.

Roger in Baltimore