"Huckleberry Hunting" as a halliard (or halyard) shanty is in Joanna C. Colcord, Songs of American Sailormen (1938; Oak, 1964, p. 65). The tune is almost the same, with 1-3 stanzas Wincing Devil posted above and a similar chorus:
Oh, the boys and the girls went a-huckleberry hunting,
To me way-aye-aye-aye-aye-i-yah
Oh, the boys and the girls went a-huckleberry hunting,
And sing highlow, my Ranzo Ray!
~Masato