There appears to be at least one other source. Jeff Warner writes in the liner notes to his album Long Time Travelling:
Stuart Frank, Curator at the New Bedford (Massachusetts) Whaling Museum, found this song in the papers of George Piper who sailed in the whaler Europa out of Martha's Vineyard in 1868. An almost identical chorus is quoted in Moby Dick, chapter 40:
"So be cheery my lads! Let your hearts never fail
While the bold harpooner is striking the whale!"
He uses the tune most commonly associated with "The Bonnie Ship The Diamond." [Link]
Warner takes after Frank in this regard, who combined the verse in Melville with Bert Lloyd's tune and text for The Bonnie Ship the Diamond, in his own 1978 recording for Smithsonian Folkways. He was apparently not yet aware of the Piper text. [Link]