Even more speculative than my usual ramblings...
As I was growing up, I would say something improper, such as repeating a word I had heard voiced forcefully upon accidentally hurting oneself, or a deliberate mispronunciation someone had used for humorous purpose, or perhaps when repeating a nasty slur someone thought they had made in private, not realizing little pitchers were in earshot.
And I'd be told "Nicht kabibble" or "ferme la bouche", each meaning "shut up your pie hole NOW" Â It was OK to ask why, but only when only the two of us were alone.
Ish Kabibble, of course was part of Kay Kayser's Kollege of Musical Knowledge; I've always assumed that nicht morphed into Ish, the way that the Tower of Babel morphed into bibble-babble, babble, and kabibble.'
Could nicht kabibble have been shortened into ishke, with the meaning of "don't babble" broadening into "don't do that with your mouth?"
I was told that Ish Kabibble took his name from a song with that title that he performed on occasion. The song in turn used a corrupted version of an old Yiddish expression "nisht gefiddelt", which literally means "it doesn't matter" or "don't worry about it", and the song does go on to address every problem with the solution "ish kabibble, I should worry? No, not me".
Ron Draney said: ... and the song does go on to address every problem with the solution "ish kabibble, I should worry? No, not me".
Whoa. That's just too close to Mad magazine's Alfred E. Neuman byline. You think there's any connection?
The Feb. 20, 1914 edition of The Jewish Sentinel, a periodical from Chicago, has this:
Origin of "Ishgabibble." This colloquialism probably comes from a Yiddish expression, "Nisht geffidelt" - not fiddled. In the olden times Jews used to hire musicians for weddings, with the understanding that the money paid was only for music till midnight; after that time the guests were to pay for the dances. The violinist was usually the leader. After midnight, when the guests were sufficiently, or more than so, full of joy, they used to dance and pay the fiddler; if it happened that one of the guests was out of money and the fiddler refused to play, the guests used to dance to the tune of a suitable song and say: "Nisht gefiddelt"- meaning we can dance without fiddling. The expression seems to be a combination of the old German "nisht" and the English "fiddled" with the German prefix "ge," and when it came into the hearing of some non-Jew, "nisht" turned into "ish" and "gefiddled" into "gabibble." [end of quote.]
I'm not sure of the sense here- a sort of heedless, amateur self-sufficiency- we don't need no stinkin' fiddles! Maybe...
It's not the same sense that deacon B suggests; maybe a little closer to Ron Draney's "don't worry about it". At first I thought "geffidelt" might be realted to an English usage of fiddle: to trifle or fuss nervously. In which case "Nicht geffidelt" could mean something like "Dont mess with it, leave it be, don't worry about it."
"This suntan lotion is no good. I drank half the bottle and I'm still just as pale as ever." - Ish Kabibble in Playmates, a 1941 movie. Â He was in 6 movies between 1939 and 1944, one of which was nominated for an Oscar.
 He admits that he got his stage name from the song Fanny Brice was performing in 1912. It was called "I should worry" but many people called it "Ish Kabibble" from the repeated use of the term in the song, but Ish Kabibble doesn't mean"What, me worry?", it means "Stop gibbering. You're spouting nonsense."  It's as if people  often refer to "The Christmas Song" as "Chestnuts roasting on an open fire", that the two names for the song mean the same thing.
Ish Kabbible wasn't happy-go-lucky Martin, he was comedic fool Lewis. Â