The “British” equivalent is a German / Yiddish word?

Also, “mum” has been in widespread use in British English since medieval times (Shakespeare has it,) whereas “schtum” is probably 20th century.

The first mistake in language is to presume that a way of saying or spelling something is unique to a region or country - often it may be used elsewhere, sometimes as a secondary form. My own background comes from seeing the differences in hiberno-english, even within a small area of a few million people - and then seeing the differences between that and "standard" english in the UK and exposure to the "english" of other anglophone countries. A problem is that language has evolved organically - and continues to evolve.

The English, unlike the French, did not set up a college to decide the correct forms and usage, so whereas the French can declare the form from a different francophone country "patois" or simply "incorrect", there is no such authority in english. IMO, this is not for a "good" reason, but just because there was an assumption that british english would always be the "mother tongue" and therefore all other forms are secondary (and a similarly arrogant assumption in the USA that "might is right"). On the other hand, language in anglopone countries with a high level of admixture through immigration, or serious exposure to another language or languages, evolves both to accommodate circumstances and in order to find a "standard" where none exists. This is not restricted to english, hence the differences between latin amarican and continental spanish - and particularly between brazilian and european portuguese.

Where it becomes problematical is where, as in the portuguese example, the usage of the "foreign" variant becomes so dominant that the orthography of the original changes to accommodate it. There is far more resistance to this in english..... so we have lots of arguments over what is the "correct" version.

It's origins are Yiddish/German but it's been appropriated in to British English.

Amongst some and apoparently from post-war prison slang.

However, as has been pointed out, mum is an old english word for silent, (from momme), hence mummers and "keep mum".

Yiddish loan words in British and American English is an interesting topic. Also, there are some English words that many people claim are from Yiddish, but actually are generally common in Germanic languages.. so not necessarily Yiddish in origin. “Nudge” is an example ..