The first one is absolutely correct, and you should feel free to use it. As far as the second one (without the contraction), it is grammatically correct, but it just sounds weird. Without the contraction, it seems like a real question, which doesn't really make sense, since the expression (in the form of a rhetorical question) is used idiomatically as a suggestion, and not a question. A related issue is "mustn't" (prohibition) versus must not (speculation or prohibition).
It's just one of those idiomatic things, like the fact that we always say "knife and fork" -- never "fork and knife."