The biggest problem with using established side characters from the show (Dukat, Garak) is the need to explain them. There will always be people going to a Trek movie just for shits and giggles, people who have never seen TNG for example. When you then do a movie about Q, they're going to wonder just who that is, without using half the movie to 'explain' Q to non-Trekkies.
The audience isn't stupid. There's nothing about the characters you mentioned that can't be explained in a very short exposition. Actually, all you need to understand is what they are (Dukat: Cardassian leader, Garak: former spy, now tailor, Q: omnipotent being) and that they have a history with the main characters. You don't even need to know what history. If it's relevant to the story, it will explain itself during the unfolding of the plot. If it's irrelevant anyway, nobody needs to know it. Seriously, it's not that hard, it happens in every single film