This is playlist I created of musical performances by people who were celebs on Pyramid. (I excluded Donny Osmond's version because they had entire theme weeks with singers.) I arranged them in order of their first appearance on Pyramid. An italicized artist did not appear on the show.
"What Would I Do If I Could Feel", Nipsey Russell, from The Wiz
"Been a Long Day", Robert Morse/Michele Lee, from How to Succeed in Business Without Really Trying
"Unbutton Your Heart", Rita Moreno, from The Electric Company (I didn't use West Side Story because her singing was dubbed.)
"Human Again", Angela Lansbury, David Ogden Stiers, Jerry Orbach, Jo Anne Worley, from Beauty and the Beast. I was surprised that I couldn't find a musical number on YouTube.
"Wilkommen", Joel Grey, from Cabaret
"Whatever Lola Wants", Gwen Verdon, from Damn Yankees
"Try to Remember", Sandy Duncan, on The Muppet Show
"They're Playing Our Song", Lucie Arnaz & Robert Klein, from the like-titled musical
"Diamonds Are a Girl's Best Friend", Carol Channing, from (I think) How to Marry a Millionaire
"Tonight", Larry Kert and Carol Lawrence, from West Side Story
"There Are Worse Things I Could Do", Adrienne Barbeau (That one surprised me, all the more so because it's a country album!)
"45 Years Medley", Gladys Knight & Clifton Davis, from a Motown special
"The Night the Lights Went Out in Georgia", Vicki Lawrence
"Stupid Cupid", Connie Francis
"Big Bottom", Spinal Tap (featuring Michael McKean)
"Nuttin' for Christmas", Barry Gordon
"Where Did the Magic Go", Didi Conn, forget the show it came from
"Blue Bayou", Audrey Landers
"My Favorite Things", Florence Henderson
"Some Enchanted Evening", Brian Stokes Mitchell, might be from the concert version of South Pacific
"Loneliness of Evening", Stuart Damon, from a TV production of Rodgers & Hammerstein's Cinderella
"Lullaby of Broadway", Ilene Graff
"You Made Me Love You", Millicent Martin
"Mean", Mark Salling & Dot Marie Jones, from a Season 3 ep of Glee
Some celebs that I couldn't find, even though I know they've done some professional singing: Fred Grandy, Martha Smith, David Garrison. Patty Duke even had a hit record. (And now I'm kicking myself for not remembering Mel Tormé.)