I dropped "My Bonnie" from my repertoire and offered it to those north of the border (I've never actually heard it on folk radio or clubs, thus far) once I became sure that it was not English but Scottish (even though I feel it's a beautiful tune). In my opinion, the origins of those two above shanties are debatable, still, and I'm yet to drop/replace them.
A couple of reasons: I love our world being multicultural, and think positive nationalism (with eco-travel and fair-trade, rather than yet more conquest and immigration) is the best way forward; and "FOLK MUSIC: Music deriving from, and expressive of, a particular national, ethnic or regional culture" (Philip's Essential Encyclopedia).