Actually, I've noticed that most of the cutscenes can be skipped. The exception is the cutscene at the beginning of each case.
Also, I wanted to add this: (MAJOR ENDING SPOILERS)
Oh, and yeah, I think I'll enjoy replaying the cases. I'll definitely turn off all hints the second time around, but I don't think I remember them well enough to take the mystery out of them. I mean, I might remember the end result, but the game is about the process and I really doubt I'll remember the specific process for any given case all that well.