From Ships, Sea Songs and Shanties, collected by W.B. Whall, Master Mariner, 3rd edition (Glasgow: James Brown & Son, pp. 1-3) [1st ed. was published in 1910]:

                      Shenandoah

    The seaman of to-day knows nothing of this old song but the tune and one line, "O Shannadore,* 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 (like Alcala in another song) "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 must be quite fifty years since it was sung as a song. 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 passanger routes, and boatmen were an important class. Shenandoah 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 heard a Harrow boy sing it. That must be nearly fifty years ago.

*"Mizzourah," and "Shannadore," were the usual pronunciations by American singers.

    This was not the only "song," by any means, which was used as a shanty. Dana told us long ago that one of the shanties used in his day was--
                   "Cheer up, Sam,
                   Don't let your spirits go down," etc.
which was made familiar to us by the old Christy Minstrels.

The 1st stanza of the version quoted (with tune) is as follows ("Oh" at the beginning is lacking):

(SOLO) Missouri, she's a mighty river
(REFRAIN) Away you rolling river.
(SOLO) The red-skins' camp lies on its borders.
(REFRAIN) Ah-ha I'm bound away 'cross the wide Missouri.

~Masato