In a bowl, combine the soy sauce, sesame oil, curry powder, turmeric, and brown sugar. Add the chicken thigh strips and toss to coat evenly. Marinate for at least 15 minutes or up to 2 hours in the fridge.
Thread the marinated chicken strips onto the soaked wooden skewers in a weaving motion so they lay flat.
Preheat the air fryer to 380F. Arrange the skewers in a single layer, working in batches if needed. Air fry for 10-12 minutes, flipping once halfway through, until the chicken is cooked through and the edges are nicely charred.
While the chicken cooks, whisk together the peanut butter, soy sauce, lime juice, honey, sriracha, warm water, and garlic until smooth and drizzly. Add more warm water a teaspoon at a time if needed.
Serve the satay skewers on a platter drizzled with the peanut sauce or with the sauce on the side for dipping.