No mention of Coming through the Rye as an alternative tune anywhere, surely? Note than the alphabetical listing of songsheets at America Singing shows The saucy little turtle. Air- "Coming through the rye." immediately after The Rebel's retort. Air- Cocachelunk. Perhaps that proximity has led to a misunderstanding.

Like Masato in the other thread, I can't place that "Irish fiddle tune". To be honest, it sounds more French to me, but who knows? If Edith Fowke knew, she unfortunately didn't specify.