Not sure what you're asking, since the sentence in this exercise obviously does use mishkefei with shemesh.
The "Hebrew construct form" (look that up online) is a "noun-noun" phrase in which the second noun modifies/describes the first noun, and is equivalent to a "noun of noun" phrase.
is equivalent to
"משקפיים של שמש"
On the other hand, If you're asking about saying mishkefei without shemesh, there are 2 answers:
..Shemesh tells what kind of glasses they are. Another kind is reading glasses, for which we use mishkefei with kriyah: מִשְׁקְפֵי קְרִיאָה
..Without any modifier, just a pair of "glasses", it's just mishkafayim מִשְׁקָפַיִם.
"proper English" is the single word, sunglasses. Over time, the 2-word phrase has become a single word, and the latter is recognized in dictionaries. A google search on 2019-12-24 found the following:
About 14,900,000 results for "sun glasses"
About 2,110,000,000 results for "sunglasses".
That difference is so enormous that a google search for
"sun glasses" definition
got the following indication that the single word is the primary spelling:
Showing results for "sunglasses" definition (About 22,500,000 results)
Search instead for "sun glasses" definition (About 1,170,000 results)
Thus another enormous preference for the single word, sunglasses. In fact, even when choosing Search instead for "sun glasses" definition, nearly all results actually used the single-word spelling!
The primary listing for "sun glasses" on various dictionary sites is:
sunglasses on these sites:
I wouldn't say such a blunt "no". Indeed these days מצרכים is only used in kitchen recipes, and there English uses "ingredients". Even-Shoshan dictionary, however, says that מצרכים are generally "household things". I'm not sure if there's a clear English parallel for that, but certainly not "ingredients". I the missing link is a time, a few decades back, when the main use of מצרכים was the things you buy at the grocery, so "groceries".
Then English uses "ingredients" for other purposes, too - notably on the label of a food product for sale. For this usage and other similar ones, Hebrew uses מרכיבים. Even for kitchen recipes מרכיבים does not sound very strange to me.