Since I am pretty much an audio-idiot, I had a very hard time with this task. Took me well over an hour. I had to backtrack a lot. Who knew I should have turned to Bette Midler instead of Neil Sedaka? The shortest route I could find is listed here.

"Weird" Al Yankovic
Dr. Demento
Big Daddy
Sha Na Na
Henry Gross
The Carpenters
Barry Manilow
Bette Midler
Mandy Patinkin
Frank Sinatra

Still, it was an interesting task.