This whaling song relates to 1890s Antarctic finn and blue whaling. The earliest texts come from Greenleaf and Mansfield's Ballads and Sea Songs of Newfoundland (published 1933). On A. L. Lloyd's liner notes:
From the latter days of whaling is this jokey remake of the Jonah legend. South Georgia lies east of Cape Horn, toward the fringes of Antarctic. Till recently there was a land station there, to which the whales were brought for flensing and processing. Presumably Paddy and the Whale originated late in the 19th century, though it's debatable whether it was a
sea-song first and a stage-song after, or t'other way round. Irish stage comedians knew it, and perhaps it was one of them who set the words to the tune of The Cobbler's Ball.
Ellen Cohn's whistled rendition is recorded on Sea Chanties and Forecastle Songs at Mystic Seaport.