I think you mean Eddie Albert from Green Acres because Eddy Arnold was a country singer and not a sitcom actor. As for Paul Lynde, I did play a song from Charlotte's Web he performed with Agnes Moorehead last year.
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Halfshell:
Specifically in this idea are sitcom stars that has recorded novelty music and not necessarily soundtrack related.
A few actors has recorded novelty tunes not related to the shows they star in.
Barbra Eden, Larry Hagman, Elizabeth Montgomery, Paul Linde (i think), Carolyn Jones, John Astin, Lorne Green, Eddie Arnold and more. I would like to see a show on novelty music by sitcom stars that aren't necessary "soundtrack" related.