This shanty, to which Hugill devotes a whole page of text describing three versions, was used with the windlass, capstan, and winches. The origin of the song is mysterious. Some believe the song originated among the early American rivermen or Canadian voyageurs. Others believe it was a land song before it went to sea. Most agree that it incorporates both Irish and African-American elements.  Two verses of the song were published in an article by W. J. Alden in Harper's Magazine (1882). He says "One of the best known of the windlass songs was the Shannandore. This is clearly of negro origin, for the "Shanandore" is evidently the river Shenandoah. In course of time some shantyman of limited geographical knowledge, not comprehending that the "Shenandore" was a river, changed the chorus. The modified song then assumed the form in which it was known to the last generation of sailors:" 

A version of was collected by R. Abrams in England in 1909. The shanty is said to date at least to the 1820s.  Shenandoah was probably an Indian chief living on the Missouri River.  Wikipedia suggests that the flatboatmen who plied the Missouri River in the early 19th century were known for their chanties, including the lovely "Oh Shenandoah".  The boatmen's song found its way down the Missouri and Mississippi rivers to the American clippers and thus around the world.  The origins of the song are unknown and there are many sets of lyrics.  Ours may tell of a roving trader, in love with the daughter of an Indian chief, who plans to take the girl with him far to the west, across the wide Missouri River.