I am currently playing a brawler that just reached 3rd level. I am playing him as an unarmed strike, disarm combat maneuver specialist. I know that is somewhat limiting, especially in regards to opponents that have natural attacks or spellcasters. Is there a fighting style that helps with disarm or combat maneuvers in general without penalizing my regular abilities? Or do I have to take multiple styles?
No, there isn't
None of the official combat style feats help with disarming opponents. Except for the third-party kusarigama-based fighting style Kusari-Ryu-Ninjutsu Style, more specifically, the second feat, Iron Tentacles
You may use any Kusari-Ryu-Ninjutsu weapon as a weapon with the disarm and trip properties.
But as a brawler, you can easily use disarm feats
There are several combat feats that help you disarming, such as Improved Disarm, Greater Disarm or Disarming Strike. And you are not required to "spend feats" on those feats, as brawlers have an ability that allows them to adjust their combat feats on demand, Martial Flexibility. And you may fulfill the requirements of "13 int plus combat expertise" by simply taking the Dirty Fighting feat.
So, even without style feats for the specific purpose of disarming, you may still use your flexibility granted by the class to create your own style, by chaining some feats that improve the disarm maneuver (and to be honest, there are few feats in that category).
Yeah, you could have spiked gauntlets of disarming, a mythril wire, or something that provides a reason to catch the blade easier than open skinned hands. Going further on the gauntlet idea, no one is remembering locked gauntlets. You run up, grab the sword, lock the gauntlets, and that's the reason he can't grab it back, either. You throw the weapon away, and then your +1 Spiked Locking Gauntlets of Disarming become the model for a disarming character. I love the concept of this. I'm making a Grappler/Disarmer that uses manacles. Grappling still allows attacks, so your second attack is disarm, then if you make your Str checks to keep the grapple, you automatically apply manacles the next round. One turn manacling at 3attacks. Grapple, Disarm, Manacles. Or, Grapple, Manacles feet, Manacles hands. 4attacks= Full manacling in one turn, without haste. Grapple,,Disarm, manacle feet, manacle hands. Disarming isn't like an attack. Like Grapple, or Shove, it's more of a "Physical Cantrip". There's always more than one use for utility cantrips, so apply that creativity. Disarming ALONE?? Weak. Planned, in conjunction with other effects?? Then, its....effective. As effective as you can make it.