It seems so counter-intuitive that the slow drawing guys can be a much bigger threat than a guy who has his guns drawn from the second you open the door!
To me it's all a matter of the division of your attention. If the second the door opens a baddy has his gun drawn you can shoot him and be done with it. With that slow drawing twit you're forced to keep an eye on him while all sorts of new customers and baddies come and go. Ignore him while dealing with other threats and he WILL eventually shoot you (once he gets around to it), shoot him immediately you'll get docked a badge, but, finally, if you really just focus too much on him somebody else will shoot you in the meantime!
Thankfully MOST of the baddies have a definite rhythm you'll eventually get down, even this slow drawer, so you'll eventually learn to just intuitively know "I'm free to ignore that guy until right about now, oh, he drew finally? BLAM!" As this might make things too easy for you, don't worry, later there are thugs with randomized timing as well as good ol' classic "You won't know if this guy is a thug or customer until he draws on you or pulls out a bag of cash."