Folk etymology
Originally, the phrase was "a whim-wham for a goose's bridle", with "whim-wham" a word meaning "a fanciful or fantastic object". The phrase was deliberately absurd as a goose would never wear a bridle. Folk etymology converted the word "whim-wham"—a word that was no longer much used—to "wigwam", an Ojibwa word for a domed single-room dwelling used by Native Americans. This change retained the phrase's absurd meaning and sense.