The songwriter's real name is Billy Edward "Edd" Wheeler (b. 1932, website: [[BillyEddWheeler.com]]). I've not seen any evidence of him being credited for songwriting contributions as "Harold Wheeler." According to Discogs.com, PeggyLee.com, AllMusic.com, and Songwriters Hall of Fame he was credited as "Hubie Wheeler" for the song "There'll Be Another Spring," co-written with Peggy Lee.
There is an unrelated notable musician named Harold Wheeler (b. 1943), who is described in the Wikipedia page as "an orchestrator, composer, conductor, arranger, record producer, and music director."