Your last posting reminded me to go back to the "Whall" reference.
Whall (first publ. 1910) gives it as the first of his collection. He's a cormudgeonly old bastard (reminds me of Conor O'Brien, who sailed around the world in the 1920's - but that's another story) with very definite views on everything. He's worth quoting in full on this one:
"The seaman of today knows nothing of this old song but the tune and one line "O Shannadore (the usual pronunciation by American singers) I love your daughter". There must be some merit in it to have lasted so long even in a debased form.
Originally it was a song, not a shanty and had nothing to do with salt water, for the "wide Missouri" is nowhere near the sea. It is given here as a good specimen of the American sea song, of which there used to be a number. It probably came from the American or Canadian voyageurs, who were great singers; Thomas Moore drew inspiration from them in his "Canadian Boat Song". In the early days of America, rivers and canals were the chief trade and passenger rouites and boatmen were an important class. Shanandoah was a celebrated Indian chief in American history, and several towns in the states are named after him. Besides being sung at sea, this song figured in old Public School collections. When very young, I haeard a Harrow boy sing it. That must be nearly fifty years ago."