Most likely, no one in the audience would have gotten the allusion, since the slang term was no longer au courant. I certainly wouldn’t have.
In line with the above, Hitler was notorious for his flatulence. He apparently had something like irritable bowel syndrome, aggravated by his vegetarian diet. After one meeting with some particularly important aristocrat and potential Party backer in the '20s or '30s, she leaned over to a servant and said sotto voce “Open a window, please. It stinks in here!”
I think I get it, this is actually like those old fashion bad words/line substitutes, like “Oh Sugar!” “Fiddlesticks” to replace Oh shit and fuck. “piece of cheese” seem to be a bad word substitute for the common insult of calling someone a “piece of shit”
“Who cut the cheese” referred to the fact that many kinds of cheese (like Limburger) are very stinky. Because of this the phrase was a euphemism for “Who farted?” Cheese wasn’t actually a slang term for crap.
I am NOT bragging, but I have an M.A. in folklore, and I actually collect slang from the past. (In the 1930s and 1940s, “Everything’s jake” meant "Everything’s just fine.) So you’re right: a piece of cheese was a fool, a jerk; but it was also a humorous euphemism for excrement.
You’ve got it, Winnipeg. In those days, “a piece of cheese” meant excrement. Today, “to slice of cut cheese” is a humorous euphemism for breaking wind. Fart.