Heat the oven to 425 °F. Soak the wooden skewers in water for 10 minutes. Line a rimmed baking sheet with foil and set a wire rack on top.
In a medium bowl, whisk the soy sauce, 1 tbsp of the lime juice, honey, oil, garlic, and ginger. Add the chicken and toss to coat. Let stand 10 minutes, or cover and refrigerate up to 1 hour.
Thread the chicken onto the soaked skewers, leaving a small gap at each end. Discard the marinade. Arrange the skewers on the rack and bake 15-18 minutes, until the chicken reaches 165 °F in the thickest piece.
While the skewers bake, whisk the peanut butter, coconut milk, rice vinegar, red pepper flakes, and remaining 1 tbsp lime juice in a small bowl. Add warm water 1 tbsp at a time, up to 3 tbsp, until the sauce is pourable.
Serve the skewers warm or at room temperature with the peanut sauce on the side.