Looking at the Corpus of Contemporary American English for phrases matching "no [n*] [vvz]" (no followed by a noun and the -s form of a lexical verb), I notice that in all the cases, the noun is singular.
No parent wants to identify their son at a morgue.
Two in 5 cases are fatal; no cure exists.
No guy likes to be lectured.
Searching for "no [n*] [vv0]" (where [vv0] is a verb not declined for the third person singular), I got phrases where the noun is always plural.
At this time, no studies exist which address the psychological skills and their relationship to skill performance in the rodeo athlete as has been documented in other sports.
Then I ask, "Has anyone here ever heard of Irving Berlin?" No hands go up.
No laws require companies to test cosmetics on animals.
This is different from sentences "none of the [n*] [v*]" for which the verb could be declined for the third person singular, or not.
None of the cases has been solved, it said.
You can bet none of the others are doing such heavy lifting.
In fact, at this point, none of the candidates is being very specific.
None of the animals were burned.