If we believe that the law of excluded middle (or the principle of double negation) is true, we must accept that every sentence is semantically both negative and positive.
When I say, "All cats are black," it means no more and no less than, "It is not true that it is not true that all cats are black." The second one is a negative sentence, in the sense that negation is the last operation that we perform in calculating its logical value. (It's a syntactic sense.) The second one is positive in this sense. But they both have the same meaning---they're semantically identical.
PS: I may have failed to answer your question. I prefer not to try solve the problem whether your "no" sentence is syntactically negative or positive. It depends on the definition, which I do not know.