Gallade
Gallade has a very high Attack stat, meaning False Swipe can do quite a bit of damage, potentially saving PP. It also gets Rain Dance to remove harmful weather conditions, Hypnosis to put an opponent to sleep, and Heal Pulse if for some reason you need to heal the Pokemon you're attempting to catch.
Scyther/Scizor
Both have very high Attack stats, meaning False Swipe can do quite a bit. Compounded with their Ability Technician, False Swipe can do quite a bit of damage, which can save you PP. Both also get Rain Dance to remove other weather conditions.
Haxorus
Using False Swipe Haxorus is essentially for the same reasons as Scyther and Scizor, minus the Technician boost.
Tapu Koko
While it may be difficult to obtain, Tapu Koko is pretty good. It has a solid Attack stat, plus it gets Nature's Madness, allowing it to cleanly cut down an opponent's HP. It can reliably paralyze with Thunder Wave, and remove hazardous weather with Rain Dance. Mean Look stops opponents from fleeing battle.
Bisharp
Bisharp sports a high Attack stat, Rain Dance, and Thunder Wave, making it an exceptionally reliable False Swiper.
Pangoro
With Scrappy, Pangoro can hit Ghost types with False Swipe. Couple that with Rain Dance and a large Attack stat, and Pangoro is also very good.
Decidueye
Decidueye has a respectable Attack stat, making False Swipe do a decent chunk of damage. It gets Sunny Day (harsh sunlight is not harmful to most Pokemon, with the exception of Pokemon with Dry Skin), plus Spirit Shackle, which prevents the Pokemon you're trying to catch from escaping.
The best user of False Swipe in this generation is probably Gallade. However, Bisharp and Pangoro are also very reliable, and the others on this list can pull their weight as well.
Hope I helped!
