The particle "on" with verbs of motion is generally used to offer encouragement to act. With a negative, a contradictory message results, so the sentence is really not possible (as already mentioned).
I too feel #2 is somehow incorrect. Maybe it is because "up" functions as an emphasizer of "hurry". But #4 doesn't seem wrong. I think "up" here is not an emphasizer but a usual manner adverb to describe the state of "stand".
I agree with Paco. "Don't hurry up", used to assure someone that there is no need to hurry, i.e., the equivalent of "Don't hurry", doesn't work. However, in a tone of exasperation, used as the negation of a previous similar utterance, it will work.
-- Hurry up! Hurry up! You're going to be late. Come on! Get going! -- (No reaction. Pause. Still no reaction.) (Sile