Use opacity instead of visibility.
For example, if want a button to fade from "Page1" to "Page2", but still want it to be visible, here is what I would do:
1. create a button
2. duplicate state
3. set the opacity of the button in "Page2" to zero
A fade effect will now appear in the "Page1 > Page2" transition.
4. In the Timeline, click "Smooth Transition" to give the Fade effect a duration
Now when the user is in state 2 the button is visibile (so it can still be clicked), but it has faded out.