Is there any shorter pronunciation of W than double-U?
Solution 1:
Sometimes if a university is located in the area which name starts with W, such university is called informally U-Dub.
This is the only case I can recall. But I don't believe that using "dub" instead of "double u" is common (or even exists) in any other context. Though I'm not a native speaker.
Here is quote from Wikipedia:
"Double U" is the only English letter name with more than one syllable, except for the occasionally used, though somewhat archaic, "œ" (its name is pronounced similar to "ethel"), and the archaic pronunciation of Z izzard.
Also, in Wikipedia, in addition to "U-Dub" example, it is mentioned that Volkswagen is also sometimes called "V-Dub".
As for the "but-why?!!" part of the question I guess nobody can answer you anything but: "for historical reasons".
Solution 2:
The letter W is known in the NATO phonetic alphabet as "whiskey". I am not sure if that counts as "semi-officially accepted" though.
Solution 3:
In Primary School here in england, the kids often say the alpheabet like ah, buh, cuh, duh, eh,fu, guh etc. rather than Ay, Bee, Cee, Dee, Eee, Eff, Gee, following that primary school notation, DoubleU could be shortened to wuh.
Solution 4:
It does describe quite accurately what it looks like - a double v or a double u.
I can't find any historical guidance on why another word wasn't used, but it isn't unique: In Spanish it is 'doble-be', where 'v' is 'be'