Combine 1/2 cup of the reserved pineapple juice with the soy sauce, oil, brown sugar, garlic salt, ginger, mustard, and pepper in a small saucepan. Heat to just a simmer and whisk until the brown sugar has dissolved. Remove from the heat and allow to cool.
Place the chicken in a shallow dish. Pour the sauce over the top, cover, and refrigerate 2 hours or overnight.
When ready to cook layer the chicken, green pepper, pineapple, and cherries on kabob sticks.
Grill: Place the skewers on a preheated grill. Cook for 15-20 minutes turning frequently until the chicken reaches the internal temperature of 165 degrees.
Oven: Preheat the oven to 375 degrees. Line a baking tray with foil and mist with non-stick spray. Cook your kabobs 20-30 minutes flipping once halfway through.