Since Dana's "Dandy ship and a dandy crew" and "Tally high ho! you know" have both been identified, I'm wondering if they are the same as these two songs, and if they are, how were they used as shanties?
First of all, "Dandy ship and a dandy crew" as found here in SONGS OF THE SEA AND LAYS OF THE LAND, by Charles Godfrey Leland, (1895) p. 104-105:
And is "Tally high ho? you know" the same as "A Yankee Ship and a Yankee Crew", found here in a book called SONG BOOK FOR THE USE OF THE COMMANDERY OF THE STATE OF PENNSYLVANIA (1883) p.18-19:
And here in a book entitled "'The Rough and Ready Songster: Embellished with Twenty-Five Splendid Engravings, Illustrative of the American Victories in Mexico. By an American Officer' " (1848) p. 200-201: