For me, the best was actually the Bob & Ray parody from the Bob & Ray Public Radio Show of the 1980s. Some of the segments of that show have been released on CD. I wonder if this sketch is among them.
Ray Goulding is the Charlie Chan character (renamed slightly to Charlie Chu or some such).
Bob Elliot is the annoying Number One son who is repeatedly insulted by his detective father. The elaborate insults are the main point of humor in the sketch.