That's interesting. Sheet music of 1846 can be seen at the Lester Levy Collection, titled 'Oh Come Maidens Come. Boat Song'. So far I'm not sure how much resemblance it bears to 'Twankydillo' tunes found in tradition, but the introductory note makes it clear that chorus and tune were based on an existing song:

'The following graceful harmony, long consecrated to Bacchanalian revelry, has been rescued for more genial and lovely associations. The words were composed for a private Boat party at Sullivan's Island South Carolina, but the Author will be glad to know that the distant echoes of other waters awake to the spirited melody. A portion of the original Chorus has been retained, which, like some of the Shaksperian refrains seemingly without meaning, lends animation to the whole.'

The 'Old Cole' form was printed by Pitts in the early C19: see Bodleian Library Broadside Ballads:

The bold farriers

'Twanky dillo' occurs, but not in the now-familiar chorus form. There were other broadside editions featuring a blacksmith instead of a farrier; those I haven't seen.

James Reeves (Everlasting Circle, 1960, 270-1) prints a brief 'Blacksmith' form noted by Baring-Gould, together with the Hallet text discussed earlier. He quotes a note from Hammond's MS: 'Final verse too indecent to be written down' - this would appear to be the one about the shepherd's daughter, so whether Frank Purslow got it from the field notebook or from another source remains to be seen.

Reeves also quotes from a version of 'The Goose and the Gander' in M H Mason, Nursery Rhymes and Country Songs, 1908, 16-17 (second verse):

The blacksmith is black, but his silver is white
And he sits in the alehouse from morning till night.
Tang dillo, tang dillo, tang dillo, tang dillo
And happy is the man that sits under the willow.

More on that song is in thread  Origins: Grey Goose and the Gander, but this is the only version with the relevant lines, which may well have wandered in from elsewhere.