Multiplayer character script control help without networking

I am working on a 2 player game that will have all of the characters on a single screen. The characters will be controlled by individual game pads/joysticks. I have a single script that controls the movement of the characters (run, walk, jump, etc.).

Currently I have two copies of this script, one for each character and I have the inputs coded into the script like this:

Input.GetAxisRaw("Vertical1"); and Input.GetAxisRaw("Vertical2");

What I would like is at run time, each player selects the character they want to control and have a script assign that character's movement to game pad one or game pad two. Any thoughts on how to do this?