In a medium bowl, whisk together the sweet soy sauce, regular soy sauce, minced garlic, ground coriander, turmeric, brown sugar, lime juice, and vegetable oil. Add the chicken pieces to the marinade, tossing well to ensure every piece is thoroughly coated, then cover and refrigerate for at least 30 minutes.

While the chicken marinates, soak your wooden skewers in warm water for at least 20 minutes to prevent them from burning on the grill. Thread 4 to 5 pieces of marinated chicken onto each soaked skewer, pressing them close together without crowding them too tightly.

Prepare the peanut sauce by whisking the creamy peanut butter, remaining sweet soy sauce, chili paste, and warm water together in a small bowl until completely smooth and emulsified. If the sauce feels too thick, stir in an extra tablespoon of warm water until it reaches a rich, pourable consistency.

Preheat a grill pan or outdoor grill to medium-high heat and lightly brush the grates with a high-smoke-point oil. Place the chicken skewers on the hot grill, ensuring they do not overlap, and grill undisturbed for 3 to 4 minutes to develop deep grill marks.

Flip the skewers and cook the other side for another 3 to 4 minutes, until the chicken is cooked through and reaches an internal temperature of 165°F (74°C). The edges should be slightly charred and caramelized, and the meat should feel firm to the touch.

Transfer the hot satay skewers to a platter and serve immediately while still steaming. Accompany with the prepared peanut dipping sauce, fresh lime wedges, and crisp cucumber slices for a refreshing contrast.