If I could hazard a guess, I'd say Redd Foxx patterned his singing voice after Louis Armstrong. It's certainly evident in a season 5 episode of Sanford & Son.
In "Brother, Can You Spare an Act?", Fred sells a used ukelele to Smiley Rogers (guest star Timmie Rogers), who promptly leads Fred in a duet cover of Nat King Cole's "'Tis Autumn". Later, after Fred's brother-in-law gets a job as a nightclub MC, Fred & Smiley perform Fats Waller's "Lulu's Back in Town", with Fred playing stand-up bass.
Now, I never saw Foxx's ABC variety show, so I don't know if he did any more singing on air after Sanford & Son ended. Meantime, let's enjoy.