In a large bowl, whisk together the coconut milk, soy sauce, curry powder, turmeric, minced garlic, grated ginger, brown sugar, and fish sauce.
Add the sliced chicken to the marinade, tossing to coat completely. Cover and refrigerate for at least 2 hours, or up to overnight.
While the chicken marinates, prepare the peanut sauce by whisking together the creamy peanut butter, soy sauce, sriracha, fresh lime juice, and honey in a small bowl.
Gradually whisk warm water into the peanut sauce mixture, 1 tablespoon at a time, until the sauce reaches a smooth, dippable consistency. Set aside.
If using wooden skewers, submerge them in water to soak for at least 30 minutes before grilling.
Preheat a grill or grill pan to medium-high heat. Thread the marinated chicken pieces tightly onto the prepared skewers.
Grill the chicken skewers for 3 to 4 minutes per side, turning once, until charred and the internal temperature reaches 165F.
Transfer the cooked satay to a serving platter. Garnish with chopped fresh cilantro, crushed peanuts, and lime wedges. Serve immediately with the prepared peanut sauce.