Stir together Dijon mustard, 1/4 cup honey, and 1/4 cup mango preserves in a small bowl to make a dipping sauce; set aside. Whisk together the apple juice, teriyaki sauce, 1 tablespoon honey, 1/2 cup mango preserves, garlic, cayenne pepper, salt, and black pepper in a bowl until blended. Add sliced flank steak and toss to coat. Set aside to marinate 10 minutes.

Preheat an outdoor grill for medium-high heat and lightly oil grate.

Remove the steak from the marinade, and discard the remaining marinade. Thread the steak strips onto the soaked skewers. Cook on the preheated grill to desired degree of doneness, about 1 minute on each side for medium. Serve accompanied by the Dijon dipping sauce.