You have the most interesting questions.
All these words are interchangeable. "Hint/sign/note" - The word note indicates that the listener is aware of the "music" of the speaker. i.e.
the phrase: "I detected a note of sarcasm," means also "I could hear a hint of sarcasm, or a sign of sarcasm in the speakers tone."
So for your sentence, all three of those words would work well.