There is an American martial art that exists in the United States of America that is based on the way that cowboys fought in the Wild West and inspires people to be quick with using a firearm for self-defense in the way the weapon is intended as well as having the weapon be used as an improvised melee weapon. This particular martial art that people can still be able to practice to this day - even if they are using modern handguns and pistols - is known as fast draw, but it is also known as quick draw if you want to use the other term.
As usual, Mint Message now has a great video on YouTube that allows you to learn about this particular martial art by watching a video instead of having to read this article, but you can still read this if it is your preferred method of learning. Gunfights in the Wild West were actually rare, but duels did happen and people did practice using firearms for self-defense just in case. A few historical individuals in the Wild West practiced forms of fast draw such as Billy The Kid and now people are doing fast draw to this day for sport as well as practice for combat.
One interesting thing about Fast Draw is that it allows practitioners to use pistols as improvised clubs in strategic ways during combat, allowing the pistol to be a traditional melee weapon even if you don't want to fire it. This is what makes Fast Draw a genuine martial art and a way for people to learn how to defend themselves when things go wrong.