No, the stats have very defined uses. The issue is not so much "shooting a gun" as it is "inflicting harm." For the most part, if you want to inflict Harm (i.e. damage) on someone, you're rolling+Hard. There are exceptions, but in most cases in which you want to hurt someone, the other moves are used to get you into a position where you can go aggro or seize by force.
One of the things that is useful to remember is that AW doesn't have "skills." The characters are assumed to know their business. As such, you can use a gun/knife/machete/blowgun/whatever with an assumed level of expertise. So when it comes to using violence, the biggest determining factor is not how skilled, fast, or strong you are, but rather how mean, vicious, cold-blooded, or determined you are. It's not about whether you have the skill to hit your target when you pull the trigger, but rather whether you have the stones to look a man in the eye and make the conscious decision to end his life. This conceptual construct is intentional, and is very much part of the "flavor" of AW.
To some extent, the construct is used for act under fire as well. So when you're trying to sneak into the enemy camp in the dead of night, the issue is not how skilled at moving quietly you are, but rather whether you will lose your shit and panic when you realize you've just stepped on a sleeping enemy ganger. If you flub your roll, maybe you freeze up, at which point the now-wakened ganger sees you and yells a warning (at which point all hell breaks loose). Or maybe you roll a 10+, keep your wits about you, and without missing a beat give the guy a kick and snarl, "quit snoring, asshole!" (at which point he rolls over and goes back to sleep because this has happened to him a thousand times before, and neither he nor anyone else in earshot thinks twice about it). Or maybe something in between.
In some sense the 7-9 range for act under fire is the metaphor through which much of AW operates. Worse outcome, hard bargain, or ugly choice - because the basic move is so nebulous, it becomes very easy to tailor this to whatever it is that the player is trying to do. With a nebulous trigger comes a flexible result, which (from the perspective of the MC) is great!
Because AW is "fiction first," the assumption is often that if you are attempting something dangerous, something bad will happen (because if it didn't there wouldn't be any drama). The question then becomes not "how do I keep something bad from happening at all," to "how do I handle the bad thing that has happened?" And that is why act under fire is so nebulous and why the Cool stat is used to resolve it. In some sense they are mechanically the same, but conceptually they are quite different and will result in different player expectations (and different narrative styles).