You'll find rather more than one tune used for different versions of 'The Handsome Cabin Boy', but I expect you mean the one that revival singers generally know (see the DT file, where there is a midi).

It's likely that a good few other songs were sung to that tune, and if it was a long time ago it won't be one of the modern parodies. What we really need is some hint from you as to what this song was about, even if you don't remember any of the words at all. That will save people just making wild guesses.