Immerse 8 long wooden skewers in water and soak for 10 minutes. Drain and pat dry.
Season chicken with salt and pepper to taste. Thread onto skewers along with bell pepper chunks and sliced squash.
Place the peanut butter, soy sauce, water, lime juice, honey, red pepper flakes, and ground ginger in a medium bowl. Whisk until smooth, adding more water to thin the sauce as needed. Reserve half of the sauce for dipping.
Brush chicken and veggies with some of the remaining sauce, then spray lightly with cooking spray.
Coat gas grill grates with cooking spray (or grill pan) and preheat on medium-high heat.
Place skewers on grill, cover, and cook 4-5 minutes. Turn and brush with remaining sauce, then cook 2-3 more minutes until chicken is no longer pink.
Garnish with freshly chopped peanuts and cilantro. Serve with dipping sauce on the side.