The version taken from the Bodleian (2, heading this thread), appears in "Scottish Students' Song Book," 1892, 3rd. Ed., pp. 126-127, with score.

At the beginning of the sheet music is "Written and composed by J. B. Geohegan. Arr. by W. H. M."
This is the first copy I have seen that is credited.

The first line of the chorus is "So blow the winds, Heigh-ho," rather than So blow the winds, I. O."

J. B. Geohagen was an American comedian, last half of the 19th c. He also wrote "DOWN IN A COAL MINE." See Edith Fowke and Joe Glazer, "Songs of Work and Freedom," 1960, pp. 47-49, with score. His music is changed in Britain to the Irish song, "The Roving Journeyman."

On p. 128 of the "Scottish Students' Song Book," is "A CAPITAL SHIP," with the note, "Words from St. Nicholas." This is the well-known childrens magazine (on line) which was distributed throughout the English-speaking world.