First question: Is this song racist? "Paddywhack," according to Miriam Webster, is dated slang for an Irishman. This website "Storytime Solidarity" has a list of sources that support that "paddy" is offensive to the Irish. The website Wordorigins goes into far more detail, listing numerous instances where "Paddywhack" is used to refer to a "stout, brawny, Irishman."
HOWEVER, this entire article ignores the use of the term "paddywhack" in the meat industry to refer to a "nuchal tendon" which makes a commonly used dog chew
True Rhymes also made a video about that.