If mám as a modal means "I ought" then why doesn't nemám mean "I need not" (I'm under no obligation to.) Here it seems to mean that you do have an obligation to refrain from action.
I agree, that the recommended sentence translates the meaning. But I think it [the Czech sentence] neither contains "should" nor "such". In other examples you used "can"[not] and "so" for both words. Can you please explain, when I have to take "can", "be suppoed to" or "would/should" ?