The letter ⟨y⟩ is largely recognized as being a vowel in specific contexts, though often disregarded when talking about vowelless words, which typically focus on the absence of the main five. A word with ⟨y⟩, but no other vowel letters, may thus be considered vowelless in this context. To a lesser degree, the letter ⟨w⟩ can act as a vowel in a narrow subset of loanwords.

chynd a. Cut into chines for cooking.
cly n. Pocket.
crwth(s) n. A stringed instrument.
cry v. Yelp.
crypt(s) n. A cave.
cwm(s) n. A valley.
cwtch n. A cubbyhole; a display of affection.
cyst(s) n. A growth of tissue.
dry(ly)(s) a. Void of moisture. n. (Plural "drys") Prohibitionist.
fly v. Move through air.
flyby(s) n. An act of flying by something.
fry v. Cook in oil.
fy i. Alternate of "fie;" Expresses disgust.
fyrd(s) n. An army.
…

I think it's ridiculous to not consider Y a vowel. Phonetically, it's almost always interchangeable with I and always makes a vowel sound.

Syzygy is my favourite.

cwm