"Ohio boating-lay..." is the closest reference I could find that does not link to the Hutchinsons. But no music or lyrics for this one either:

“Scene, the Thames. The Tipperary skiff is making her way with the tide. EVERARD CLIVE and the TRAVELLING BACHELOR are at the oars; the WHISKEY-DRINKER and the FENMAN are in the stern-sheets.

WHISKEY-DRINKER.
Ease off a little, Everard––the tide will carry her on––and give us some of your conversation, such as it is.

EVERARD CLIVE.
Easy it is. We'll just give a stroke or two to guide her, and draw it mild down to Kew. Bachelor, you will not object to a little “otium cum dignitate,” I suppose.

TRAVELLING BACHELOR.
Certainly not. We, “Laboriosi remiges Ulyssei,” have brought her smartly enough down from Twickenham. Drinker, give us the Canadian boat song.

EVERARD CLIVE.
Let us have something a little more novel. The Ohio boating-lay for instance. Or is there any song from the Oregon streams? I wonder whether the Yankees will get up any boat-races on the Columbia.

FENMAN.
They must get possession of it first, which will not be effected quite so easily, in spite of all the blustering of their press and orators. These “Sweet creatures of bombast” are like Falstaff, more prone to the exercise of the tongue than of the sword.”
[Tipperary Hall, No.V, Bentley's Miscellany, Vol.19, 1846]