In a large bowl, whisk together 1/4 cup peanut sauce, kecap manis, oil, lime juice, salt, and lime leaves until fully combined. Adjust seasoning if needed.
Add the chicken cubes to the marinade, ensuring all pieces are evenly coated. Cover and refrigerate for at least 1 hour (or up to 24 for maximum flavor).
Thread marinated chicken onto skewers, packing the pieces tightly toward one end. Reserve the marinade for basting.
Preheat the grill. For charcoal grills, set up a two-zone fire by banking coals to one side. For gas grills, preheat to medium-high heat.
Place skewers over the hot zone and grill, turning frequently and basting with the reserved marinade, for 5-8 minutes or until lightly charred and fully cooked.
Transfer finished skewers to a serving plate, cover with foil, and continue grilling the remaining batches.
Serve grilled chicken satay with cucumber slices, fried shallots, and a small bowl of peanut sauce for dipping.