Thank you to all who have contributed to this thread; and especially to Stuart Smyth for attributing it to Iain MacCarthaigh and providing the recording. It was very interesting to listen to, because I see that the version I learned (from someone from Dublin) has been subject to the drift of 'the folk process'. The tune I learned is the same, but I heard it sung quite a bit faster, and there's an addition of a chorus (not on the recording), and the story has been retold so that it is the captain who is killed, rather than one of the men taken on board. In essence, it's kind of morphed into a drinking song, and isn't too bad for all that. Having now heard the original words in the recording, I have to admit that I plan on sticking to the retold story - just because I tend to stick to singing things as I learned them, keeping to the idea of the folk process being an original sing.

I thought I'd just throw the words that I sing into the thread, not to claim they're 'authentic', but just because the variation from the recorded version may be interesting to some people.

Billy O'Shea (Dublin song, in the style of a long-haul shanty)

Well, we all got drunk in Dublin city
Fall down me Billy!
Well we all got drunk and more's the pity
Fall down Billy O'Shea!

Chorus:        And it's fall down, fall down,
       Fall down me Billy!
        And we'll all get drunk in Dublin city
        Fall down Billy O'Shea!

We lay ourselves down on Rogerson's Quay
Fall down me Billy!
And when we awoke we were out at sea
Fall down Billy O'Shea!

We are not sailors, captain dear
Fall down me Billy!
We come from land and we won't work here
Fall down Billy O'Shea!

So we swung him up to the topmast yard
Fall down me Billy!
Well he hit the deck, and he hit it hard
Fall down Billy O'Shea!

And we wrapped him up in a big white sheet
Fall down me Billy!
Threw him overboard for the sharks to eat
Fall down Billy O'Shea!