Flake salmon, including juices into a large mixing bowl. Add celery, carrots, nuts, red and green peppers, onion, egg, lemon juice, salt and pepper. Mix gently to combine.
Form 6 to 8 cakes that are 2- to 3-inches around. Pour panko into a plate. Press panko to coat the outside front and back of each cake.
In a medium sauté pan, heat oil on medium-high. Place 3 to 4 cakes in the pan, and cook for 3 minutes, or until golden brown. Flip over and cook 2 minutes more. Remove from pan to cool on a rack or plate.
Add another tablespoon of oil if the pan seems dry. Cook remaining batch for the same length of time. Serve immediately.