I don't know how it is in the British Isles, but from my American perspective, "chink" (when referring to the Chinese), like "nigger", doesn't really have any harmless applications. If I were to sing this song, where the wordplay with "chink" meaning gap cannot be approximated with any other word, I would preface it with an explanation to the audience.

I have heard "Yankee" used somewhat (or very!) derisively by American Southerners in reference to American Northeners. I have "Yank" used rather universally overseas to refer to all Americans. Very seldom do I see the forms switched around.