I remember watching some behind the scenes training stuff. I believe it was more jujitsu and judo (which is a derivative of jujitsu) in his training and it looked like it on screen. He moved like a judo-ka. If there was any Brazilian Jujitsu it was a minimal influence. Go back and watch the fight with the chick in the hotel room. The trainers and coordinators specifically mention she was a trained in Brazilian Jujitsu (which is actually a derivative of Judo if you trace the history) and she looked very much like it. If you want a good comparison/to see the differences between jujitsu and judo vs BJJ then that's an excellent scene. Similar, but subtle and notable differences. It was a brutal and effective martial art that was born on the feudal battlefield. When you had no weapon and had to kill an armed and armored opponent the hand to hand combat used was ruthless. It's very fitting to the character.

It's also further reinforced by the tattoo on his back linking him to a Hawaiian Marine Corps unit and his own Hawaiian heritage. There was (and still is) a large Japanese population and amount immigration to Hawaii, especially around the time Japanese martial arts started proliferating outwards around the end and shortly after the Meiji Restoration. Japan was previously very isolationist and Hawaii was its stepping stone to the US.

John Wick has an incredibly rich background for being an action movie that just keeps chugging along. They created a lot of depth in almost every aspect to a movie with a simple premise and plot. Despite being an action movie that uses cars a bit and relies heavily on 'gun-fu', John Wick is probably one of the best martial arts movies in existence. It was technically brilliant with amazing cinematography. The stunt team and choreographers managed to integrate it into the gun-play so well and seamlessly transition between them. The screen is never 100% accurate to real life but I never saw a point where I though "that's gratuitous/unreasonable". The team they had weren't just actors; they knew what they where doing across the board. They brought back a lot of the team from The Matrix (the directors of John Wick worked the stunt team on The Matrix and have experienced careers. They knew exactly how to put John Wick on screen) and holy shit did they deliver.