CK,

Salty Dick is sorta presenting it as one-man entertainment-comedy, hence the instrumental. It's a musical choice. So be it. In that case:
After you pick a key, identify the I, IV, and V chords. For example, if you're in key of C, then C, F, and G(or G7) chords. Then just sing and strum one of those chords. If it sounds good, you've got it! If not, pick another. To start you off, it sounds like the verses begin IV I IV I ...

On the other hand, as this is my rather crusty idea of chanty-singing—and the picture a vision of a scene it evokes in *my* mind— I have difficulty imagining anything strumming along with it! Most chanty singing was described by contemporary observers as "plaintive," "mournful," "wild" and so forth.

On the other other hand, if you think my vision of a chanty is pretty dull, take this one which is more fun!—but still required no chordal accompaniment to be great.