Well, I don't remember Wally Cox being in The Amazing Mr. Limpet, Don Knotts was the star there, I think. Cox (1924-1973) was most noted for his starring role in the TV comedy, Mr. Peepers, though he was in quite a few movies as well. I especially remember the line Gee, Wes ~~ frequently directed to costar Tony Randall, a line we used often as kids when we wanted to express incredulity.

As far as his music is concerned, that was pretty much it. I don't recall any other recordings by him. Nor could I locate too many current recordings of the song, Sam Hinton, PEI fiddler Sidney Baglole, Six Fat Dutchmen, Roz Brown, Organist George Wright, Rudy Vallee and Burl Ives, in varying degrees of availability, are just a few to look for.