Since the question of how you should spell this word seems to be a matter of opinion, I will focus in this answer mainly on describing what kind of precedents there would be for either choice.
The sequence "quu" does occur in "equus" and "obliquus", which are not exactly English words but are pretty well-established in phrases used in English.
That said, there also seem to be some somewhat established words that use "qu" for /kwʊ/ (or perhaps in some cases /kwʌ/), which surprised me. Merriam Webster lists "squushy" (a variant of "squishy/squashy") but says it is also spelled "squshy". Infoplease and Dictionary.com also have entries for "squushy", with that spelling.
A look at the Google Ngram Viewer indicates that both spellings have been around for a while, and although I don't think either is frequent enough to make a really confident statement about which one is more standard, "squshy" doesn't seem to be noticeably less common or more recent:
The spellings "sqwushy" and "skwushy" don't appear to have any usage.
Google Books also provides some concrete examples of "squshy":
we boys used to pick the squshy pawpaws when we went swimming in "the creek".
(In Portia's Gardens, by William Sloane Kennedy, 1897)
Or he reposes on three or four feather beds piled one upon another, a patchwork quilt being spread over the squshy mountain.
The Century Illustrated Monthly Magazine, Volume 41, November 1890 to April 1891
The leaves on the forest floor were thick and squshy with who knows how many years of leaf build-up which offered a crunchy but soft cushion for my small feet and their little paws.
More Adventures of Bruno and Bowser, by Stephen B. Hughes
I wasn't able to find any words that seem to be in anything approaching common usage spelled with "qwu" via OneLook Dictionary search (all of the results on that page seem to be acronyms or Urban Dictionary entries that were just made by some random person).
So on the one hand, "qu" and "quu" do have some prior usage in "squshy"/"squushy", but since I would pronounce that /skwʊʃi/, it may not actually make the pronunciation as clear as you want it to be. That said, the "sh" in that word may also be relevant to the pronunciation of the vowel, as /ʊ/ seems to be more common in this context than before other consonants: compare bug, buzz, bus and bush, bushy, bushel; pug, pus, puzzle and push, pushy; or mug, muzzle and (for some, although not most, speakers) mush, mushy. So it may be that "qu" would be likely to be interpreted the way you want it to be, as /kwʌ/, in the different context of "squzzle".
The spelling "quu" has, as I mentioned earlier, precedent in words from Latin (or Latin words used in English), but I don't actually know of any cases where it represents stressed /kwʌ/ with stressed /ʌ/; in the examples I mentioned earlier, the "u" represents an unstressed vowel probably best transcribed as /ə/, and in the constellation name Equuleus, the only example I have found so far where the vowel is stressed, it is pronounced as either /uː/ or /ʊ/ depending on what dictionary you check. (The use of /ʊ/ rather than /ʌ/ can be explained in this word as well as at least partly conditioned by the following consonant, in this case /l/; consider pull, full, bull). The best I can come up with is that some people might pronounce the Latin word "sequuntur" with /kwʌ/ in an English-language context (apparently, "non sequuntur" has been used, rarely, as a plural of "non sequitur"), athough with the rise of reformed pronunciation it's hard to say whether /kwʊ/ or /kwu/ might be used instead.
The fact that "qwu" doesn't occur in any commonly-used word could be seen as a disadvantage, but it also means people might not have preestablished incorrect expectations about how to pronounce it.