Wonderful discussion.
With apologies for my poor spelling, I can't recall the boys ever using "tuccus" or "schmuck." Would these have been too politically/socially/morally inappropriate for the time? I can recall from my youth that, for a while, they would edit out (on TV) the black baby who "looks just like the Captain" from a scene in Uncivil Warriors (I think).
Lastly, I just have to ask this where someone might actually know the answer -- what is the plural of "tuccus," would it be tucci or tuccuses. Just wondering.
"Tucci" is the name of an American movie actor of Italian descent.
The short answer is that you should use the regular English ending to form the plural. The long answer is as follows:
The unstressed final syllable [ɘs] in Yiddish, which may be represented as "-us" in Roman characters, has nothing to do with Latin nouns whose endings are spelled that way: the spelling "es" is just as apt, and is often used. In any case, Yiddish does not form plurals according to any Latin model. (Nor, for that matter, do all Latin nouns ending in "-us" form their plural with the ending "-i"; but that's another story.)
The consonant in the middle of the Yiddish word in question here is conventionally represented in English as "ch." (In phonetic terms, it is a voiceless velar fricative, represented in IPA symbols as {x] (I had to use "{" instead of "[" because of a compiler problem there); but I don't expect that information to be of much use to anyone reading this.) Hence the spelling "tuchus," "tuches," "tochus," or "toches" would be more accurate. (The vowel may be either [ʊ] or [ɔ], depending on the dialect.)
The Yiddish noun is derived from the Hebrew word "tachat," which is spelled with the same consonant letters (viz., תחת). I am not sure if it admits of a plural in Hebrew or in Yiddish, because it is originally an adverb (meaning "under"). In any case, since you are writing in English and neither you nor your readers know Yiddish, you should use the English ending to form a plural: "tuchuses"---or "tucheses," "tochuses," or "tocheses."
I am pretty sure that "tuches" is not a naughty word, but rather a bit of nursery talk, like "botty" (from "bottom") in British English. I don't know of it occurring in any of the Stooges' shorts, but it would not be beyond probability that they would use it somewhere. "Shmuk," on the other hand, is a decidedly rude adult word (it refers to the penis, by the way, in case you didn't know), and I would be greatly surprised if it turned up in any motion picture made in the US before the 1960s, say.