I play a Temple of Mystery and puts the scry card on the top of my library. My opponent then casts Dreadwaters targeting me, with X = 4. I can put those four cards in my graveyard in any order (CR 404.3). Can I shuffle those cards before revealing them, to conceal which card was the one I scried and deny my opponent information? Or is my opponent entitled to know which card is which?

Does the answer change if I'm targeted instead with Ashiok, Nightmare Weaver's +2 ability?

Your opponent is not entitled to know the original order of cards that you exile or put into your graveyard from your library. They go directly from being in order in your library, where your opponent can't see them or their order, to being in a different order (or no order at all) in the zone they're moving to. At no point does your opponent see the previous order.