What about having 25 scrabble-like squares in a bag, and the spymasters pick randomly in the bag. Each square has a number from 1 to 25 that correspond to one position on the 5x5 grid, and one extra square is chosen to be the black square and shown to the spymasters. The spymasters have a pen and a piece of paper with a 5x5 grid where they can mark the information they receive.
(that is if the spymasters are not informed of the position for the other team, I'm not sure if it's the case or not in the real game. If not, it's even simpler: both spymasters look at the result of every pick, the squares are colored and the order in which they are picked is the order they are on the grid)