I would think that "Nick nack paddy whack" is like "Davy Davy Nick Nack", just a very successful marrying of nonsense syllables to a memorable bit of tune. Whether in the dim and distant past there may have been some unfortunate Paddies getting whacked in an early version I couldnt say, but I doubt if that is in the minds of many of the children who delight in singing it. But it could become that way, if someone uses the internet to start a legend that that is what the song is about, and then it will become a de facto anti-Irish song. Such things gave happened.