Y'all would probably enjoy Wikipedia's discussions of English phonotactics:
https://en.wikipedia.org/wiki/Phonotactics#English_phonotact...
https://en.wikipedia.org/wiki/English_phonology#Phonotactics
/ʃm/ is not a legal onset in native English. (Let alone /tʃm/, which is how I pronounce "chmod" - two syllables, /tʃə 'mɔːd/.)
"Schmear" is a Yiddish loanword coming from German, where /ʃm/ is perfectly legal. So it's pronounceable by the human mouth, it's just a little awkward for English speakers.
/sm/ and /ʃr/ are both legal in English, so you might think of it as something like those. Can you pronounce "smear" or "shrine" as one syllable?
(I'm not sure /tʃm/ is valid in any language - words or names that start with "chm" seem to be Polish/Russian words transliterating /xm/.)