I've done some searching for this before, but I don't think I came up with an answer...
I saw a 1930s cartoon-- one of those with various "celebrity tribute caricatures"-- and there was a reference to Eddie Cantor having a scar-- or perhaps "surgery" was mentioned.
I didn't find anything at the time, so I figured he might have been one of the many people in earlier times who had undergone an emergency appendectomy, and it had made news across the country.
Now I've seen a short where the real Eddie gets pulled over for speeding, and when the cop doubts his identity, Eddie offers to show his scar. It SEEMED like he was indicating too high on his body for the appendix, but maybe I misinterpreted his move to unbutton his coat.
Again I've searched various combinations of words on Google, but I'm still in the dark...
(Yes, I know he had heart problems, but I think that came at least a decade later. And how many heart surgeries were available wayyy back then?)