Do you know of any, other than:
NTH - as in “To the nth degree”
SH - an urge to silence
CWM - a shallow valley
?
rhythm
http://domin.dom.edu/depts/gslis/stumpers/faq.html
Brrr: The sound of shivering
Crwth: An ancient stringed musical instrument
Cwm: A cirque (a steep-walled mountain basin shaped like half a bowl)
Grr: The sound of a dog
Hm: An interjection expressing assent
Hsh: An interjection used to urge silence
Nth: adjective pertaining to an indefinitely large number
Phpht (pht): An interjection used to express annoyance
Psst (pst): An interjection used to attract someone’s attention
Shh (sh): An interjection used to urge silence
Tch: An interjection expressing vexation or disgust
Tsk: An exclamation of annoyance
Tsktsk: To utter tsk
Tst: An interjection used to urge silence"
Notice no Y’s included. 
That one where the “…and sometimes Y” rule applies. There’s lots of those: CRY, TRY, etc.
Ng: a surname.
Wff: a proposition in formal logic.
“cwm” and “crwth” aren’t actually vowelless. They’re just foreign words, in a language (Welsh) in which “w” is a vowel.
If we are going to exclude words used in the “American” language that have foreign origins and/or influences, then we aren’t going to have too many words from which to choose, are we?
Sorry, typical self-centered ugly American syndrome at work here. Assuming everyone here is US…
So, AWB what are the rules here? Languages? timelines? cultures? etc. 
Suzee Vlk, of whom I learned when she appeared on Jeopardy!
I once knew a man named Edward Srp.
Syzygy
Vlk means ‘wolf’ in Czech and Srp means ‘sickle’ in Serbo-Croatian.
Guess what: in some Slavic languages, l and r can function as vowels. They’re called “vocalic l” and “vocalic r”. The vocalic l and vocalic r also existed in Sanskrit, where they’re classed as vowels, not consonants. These go back to Proto-Indo-European. So those names don’t count as vowelless. They only look that way. English, in fact, also has vocalic l, in words like bottle, trouble.* The final vowel sound is made in the l position. There is no other vowel sound except that made by the l forming a syllable of its own.
Syzygy obviously isn’t even in the running.
Why?
Why what?
Basically, words that can be used in Scrabble: non-proper (uncapitalized), non-hyphenated, non-contraction. On the inclusive: English names of foreign letters, English names of foreign currencies; Welsh, Scottish, Irish, American, and Australian words.
According to some theories of speech perception (cite), it might very well be impossible for words to exist without vowels (in speech, that is, spelling is a different game).
Only utterances with vowel sounds in them can be recognised as words. I don’t know whether they would make an exeption for things like '“shh” , or just say that that wouldn’t be a word.
“Jomo Mojo: Why what?”
That’s why…who’s on first
Why = Y AWB What letters are considered vowels? I’ve heard y & w count as vowels in some cases.
“Y” is a vowel when it makes a vowel sound. See words like “cry”, “try”, “tryst.”
What is a vowel? Well, according to Merriam-Webster:
“W” is only a pure vowel when it makes the “oo” sound, as in “cwm.” In American English, there is no word I can think of in which “w” is a pure vowel. However, letters such as “w” and “y” when treated as consonants, are really semi-vowels, or glides.
I’m sure Jomo will be in soon with a technically precise distinction.
pulykamell explained it so well, I can’t think of anything to add. Just remember, MaryEFoo, that things like vowels and consonants are sounds. The letters of the alphabet used to spell them are irrelevant in linguistics; you have to look at the sounds and ignore the letters. Then you will understand what a vowel is and what a consonant is.
I appreciate the M/W input. Perhaps I should have been more specific? What constitutes a vowel according to the OP’s recent ruling.
“Basically, words that can be used in Scrabble: non-proper (uncapitalized), non-hyphenated, non-contraction. On the inclusive: English names of foreign letters, English names of foreign currencies; Welsh, Scottish, Irish, American, and Australian words.”
If we include all the countries listed and the vocabularys thereof, the words included in the list should be interesting.
Was Canada included? They are UK related…right? or are they more closely linked to France…
Incidentally, I’ve never seen “cwm” used unquoted in a sentence. Oh, sure, I’ve seen “You know, ‘cwm’ is a word,” but I’ve never seen “Let’s go to the cwm.” Has anybody ever heard “cwm” used unquoted in the USA?
There was a bluff we used to climb on outside Ottawa named the western cwm after the rather more famous western cwm by that big hill over in Nepal… So when I was living there we used it all the time, pretty much exactly in the sentence ``So, shall we head to the cwm’’. Of course, Ottawa isn’t in the USA exactly, but it’s only a couple of hours drive away. Does that count?