St. Anne, a.k.a. St. Hannah, was the mother of the Virgin Mary and grandmother of Jesus. She is also the patron saint of (among other things):
against poverty, Brittany, broommakers, cabinetmakers, Canada, carpenters, childless people, homemakers, housewives, grandmothers, grandparents, lace makers, lace workers, lost articles, miners, mothers, old-clothes dealers, poverty, pregnancy, pregnant women, Quebec, Santa Ana Indian Pueblo, seamstresses, stablemen, sterility, Taos New Mexico, turners, women in labour
"Holy Hannah!" just might
be an exclamation characteristic of one of the above groups. This saying then may have spread to the general public.
The source I cited also notes that Canadians considered Anne to be the patron of all who travel by water. Is the phrase another example of sailors' jargon? (Some other examples would be "taken aback," "know the ropes," "scuttlebutt," "take the wind out of one's sails.")
But then again, I have no idea . . .