The word shtum was intoduced into Yiddish from the German word stumm meaning silent. The phrase keep shtum (variously spelled ‘keep schtum’, ‘keep ‘keep shtoom’, ‘keep stumm’ etc.) came into the English language quite recently.
The earliest citation of it in print in English is in Frank Norman’s, book Bang to Rights: an account of prison life, 1958, although colloquial uses of it may be much earlier:
“I think it’s much better to keep shtoom.”
“You can always shtoomup if any screws are earholeing.”
“The screws [prison officers] word is gospel, so as well as getting done for the snout you get done for making false accusations against a prison officer, so there you are the best thing to do is to keep shtoom otherwise you’ll wind up bang in trouble.”