I've taken time to read the entire thread, and there are some very good answers here. Balancing cultural sensitivity (with or without a political correctness component) against historical accuracy is difficult. Humming the line is one possibility, explaining the context to the audience is another. Educating the audience isn't a bad thing. And the suggestion to just not sing them if you feel compelled to change them is also a good answer. Ours is no longer a culture that will lose songs in one generation if they aren't sung. They're written down and recorded.

Objectifying an entire race or culture by applying a slang name to them is part of the human condition. It wasn't invented by anyone in this generation of humans on the planet, and it won't be discontinued by this generation. Places like Ellis Island were where the rubber hit the road in Euramerican cultural biases. Some very powerful Social Darwinists influenced immigration legislation in the few decades after the turn of the last century. If anyone really wants to examine this end of the question, look at Donna Haraway's essay "Teddybear Patriarchy" in _Primate Visions_. Bigotry knows no boundaries, this is just one example. My family dropped the "O" in O'Dwyer around the mid-1800's when a general cultural attitude was "no Irish need apply."

Enough preaching to the choir. In public, if you can't sing it comfortably, if you are a purist but don't feel you have the moral authority to sing it without modification, then leave it to someone else. If you feel comfortable being part of the folk process, and changing meets your needs, then sing it. Either way, someone will be unhappy.