Alway liked Mahi Beamer's version of the "Wedding" song, with the wonderful voice breaks. Anyway, I think that "My Little Grass Shack..." is a real Hawaiian song--here is the note on the lyrics at the Hula Archive(Huapala) linked in Mark's post--

Source: Noble's Hawaiian Favorites, Copyright 1933, 1961 Miller Music Corp, Hawaiian Music and Musicians by George Kanahele, University Press of Hawaii, Library of Congress Catalog #79 14233. - Based on an old song "Back in Hackensack, New Jersey", composed by Art Beiner and Dan Russo in 1924, this was first heard in Kona, Hawaii at the July 4th canoe races, 1933. Harrison gave the song to Johnny Noble to publish, who revised the music to give it an almost new melody without changing Cogswell's words. This was done to dispel the claim that others had written the song. Once published, the song became a smash hit. Noble turned over the royalties to the Sherman Clay Co in San Francisco for $500.00 advance royalty, giving the credit to Cogswell and Harrison. Kealakekua is the bay where Captain Cook was killed in 1779. Honaunau is the ancient City of Refuge and Kona is the district where both are located on the Big Island.