You won't find it in the Penguin, don't know about the Oxford. Hugill gives "Tommy's gone to Hilo town" as a first line and another variant as "Tommy's gone on a whaling ship". But there's no "right" version, every shantyman would have had his own version, and they were semi-improvised.

As we know, anyone can put stuff on the internet without knowing anything about the subject. I'd sooner rely on Doerflinger and Hugill than on something found by googling.

And Barry Finn is right, shanties came from a multi-national culture, just because they're in the English language doesn't make them "English" in the sense WAV wishes for.