What Hugill said-
Drunken Sailor- "This is a typical example of the stamp-'n'-go song or walkaway or runaway shanty, and was the only type of work-song allowed in the King's Navee."

In other words, Hugill was referring to a type of shanty, not particular songs. Stan Hugill, "Shanties from the Seven Seas," 1961 (and reprints), p. 108.

He explained further in 1969 that these were played by fifers and fiddlers when heaving up the anchor aboard naval vessels, but there was NO singing at the chore. "Nancy Dawson," "Drops of Brandy," and "Off She Goes" were played (reference given).
Whall was the source of the statement about "Drunken Sailor" and "Nancy Dawson" being sung on revenue cutters and smaller fighting craft, but Hugill says there is no literary proof of this.
Stan Hugill, 1969, "Shanties and Sailors' Songs," pp. 9-10.