Actually, I think this needs to be a mini-game. A couple of feats or combat styles isn't going to do the trick; Bagpuss is right, you need to revamp whole sections of rules.
No character classes: go with CoC's "Offensive" vs "Defensive" types, with a bunch of starting packages of skills for various occupations. Though I'd strip down the skills list, too; you don't need Survival or Decipher Script here.
Good chase rules (hey, I'm writing a set of those. Huh.), no AoO or any battlemat-related stuff. Not tons of feats, either -- in the genre, anyway, people aren't usually recognized for one kind of maneuver or another (unlike kung fu movies) -- everybody seems to be able to slide down a staircase backwards, blowing away bad guys. So you need a set of combat maneuvers or modifiers or some way of codifying (not too much, not too little) the cool n crazy things characters can do.
Maybe have a "Panache" score that you can use up for certain things (like add it to your Initiative -- when you're full of cool, nobody gets the drop on you).
One problem is that the genre is largely lone-wolf: there's the ending of A Better Tomorrow II, though, where our three heroes walk into the bad guy's lair. And then everybody dies (That should be the mandatory title of every last act of every published Gun Fu adventure: "Chapter Seven: And Then Everybody Dies"). So that'll work, I think.
You need it to be a game where players will ACTUALLY walk into a house populated with DOZENS of bad guys, even though it's almost certain death for them.
And there's the whole "ran out of ammo" thing. Instead of worrying about how many rounds are left in your gun, there ought to be a means of deciding when to run out of ammo. Like you can spend Panache points to make your OPPONENT run out of ammo. "Click." Or you can spend Panache points to make sure you've got ONE ROUND LEFT. "Bang!"
Tossing guns is obviously VERY important. And it's always faster to run on top of the tables instead of around them.
Characters won't be as differentiated from each other as in most d20 games. The fun isn't in filling in the boxes on your character sheet; it's making up cool stuff on the fly.
DMs will need to have a means of defining environments so as to encourage coolness. Instead of maps you want "Features" and the coolness that can emerge from them.
Huh. I want to write a Gun Fu minigame. Stand by.