Should "We don't want sleep" work? Google translate indicates that "slapen" is also a noun for "sleep" (I guess like eten is "to eat" and also "food")
It also wouldn't work because if you meant the noun version of "slapen", you would have to use geen instead of niet. Niet negates verbs, geen negates nouns.
"Wij willen geen slapen." And as vam1980 pointed out, it would mean we do not want temples (anatomical), which nobody in their right mind would say.
No. 'Slapen' is actually a noun, plural of 'slaap', but it means something entirely different: 'temple' (the part of your head that's to the side of your eye). 'Slapen' is definitely the verb here.