I was an equipment manager for the team back in the Mackovic era. We would wipe the game balls down with a wet towel. The quarterbacks would let us know how they liked them for the games. Mackovic liked to have clean new balls for the games, but Shea Morenz wanted old balls that were very broken in. Sometimes we would paint the stripes white to make them look newer so Mackovic would be okay with them. Morenz also liked to have the balls deflated a bit, so after they were checked by the refs and given back to us we would take a little air out on the sidelines.
James Brown could care less, he would play with a ball right out of the box and not worry about it.
We would also have kickers balls for game day so the kickers and the punter would check the balls too. Phil Dawson liked them a little deflated. One time he got phlebitis in his foot and claimed it was because the balls were aired up too much.