I'm a big fan of keeping it simple. Just have them roll initiative and add a boost die for Quick Draw or any other applicible talents. The default initiative skill I'd use would be Cool, but if the player can come up with a convincing reason to use some other skill, such as Vigilance, then I'd allow it.
I might leave room for other factors to modify the roll. If someone hasn't been in a dual like this before, make a fear check. Are they a gun expert, by having more ranks in Ranged Light than their opponet, thus showing how competent they are with their weapon, then give a boost die.
Remember, if you want to be good at a fast draw you should be a Scoundrel. A Scoundrel doesn't win initiative by having a high Cool skill alone. A Scoundrel who wants to will gunfights will invest heavily in Rapid Reaction to buy extra successes in initiative. Rapid Reaction is why the Scoundrel is the quick draw master in the main book.