Really?
Using two controllers for black and white separately means that your software is able to manage two players at a time, each one with his own controller.
OGS doesn’t do that, nor does it any SGF client or PC Go software that I know.
There are many apps that allow you to reproduce a game, hence to play a new one, but controls are for one person (keyboard and mouse).
So I think you actually need a different kind of app, which behaves like a multiplayer game instead of a simple Go client.
I actually installed a Go app on my Xbox. It’s a KGS client and I used just once. Probably you could find something similar for your PS4.