Combine chicken thighs, 3/4 teaspoon salt, white pepper, and sunflower seed oil in a bowl. Cover and refrigerate for 1 to 2 hours.

Soak wooden skewers in water to prevent burning during cooking.

Bring water, peanut butter, kecap manis, brown sugar, garlic, and 1/2 teaspoon salt to a boil in a small saucepan; stir to combine. Remove from heat and add lime juice; transfer peanut sauce into a bowl.

Thread marinated chicken onto skewers; brush 2 tablespoons of peanut sauce over chicken skewers.

Heat a grill pan or large skillet over medium-high heat. Arrange chicken skewers in batches on the grill pan and cook until chicken is no longer pink in the center, 1 to 2 minutes per side. Serve skewers with remaining peanut sauce.