Toss pork and salt together in large bowl and let sit for 20 minutes. Meanwhile, whisk ketchup, sugar, chili powder, cornstarch, liquid smoke, and cayenne together in bowl. Set aside 1½ tablespoons ketchup mixture.
Add remaining ketchup mixture to pork and toss to coat. Thread pork onto four 12-inch metal skewers, leaving ¼ inch between pieces. Spray both sides of meat generously with oil spray.
FOR A CHARCOAL GRILL: Open bottom vent completely. Light large chimney starter filled with charcoal briquettes (6 quarts). When top coals are partially covered with ash, pour evenly over half of grill. Set cooking grate in place, cover, and open lid vent completely. Heat grill until hot, about 5 minutes.
FOR A GAS GRILL: Turn all burners to high, cover, and heat grill until hot, about 15 minutes. Leave primary burner on high and turn off other burner(s).
Clean and oil cooking grate. Place skewers on hotter side of grill and grill until well charred, 3 to 4 minutes. Flip skewers, brush with reserved ketchup mixture, and continue to grill until second side is well charred and meat registers 140 degrees, 3 to 4 minutes longer. Transfer to serving platter, tent loosely with aluminum foil, and let rest for 5 minutes.