The songs that were cut, with writer credits (this does not mean the writers own the songs, of course):
Wayne and Wanda:
Stormy Weather
Words and Music by Harold Arlen
Recorded by many, many people, including Cab Calloway and Ella Fitzgerald
Jim Nabors #1:
Gone With The Wind
written by Herb Magidson and Allie Wrubel
Recorded by Horace Heidt (#1 in 1937)
for the Danceros number:
Bye-Bye Blues
Words & Music by Fred Hamm, Dave Bennett, Bert Lown & Chauncey Gray
Recorded by Bessie Smith, 1924
The Paul Williams opening number:
All of Me
Words & Music by Seymour Simons & Gerald Marks
Recorded by Frank Sinatra, 1952; also recorded by Willie Nelson
Charles Aznavour #1:
The Old-Fashioned Way
Written by Charles Aznavour
Recorded by Charles Aznavour
Vincent Price final number:
You've Got a Friend
Written by Carole King
Recorded by almost everyone in the entire world, including James Taylor
There you go.