Soak skewers in water 30 minutes. Meanwhile, trim ends from pineapple, then stand it upright and cut off peel. Quarter pineapple lengthwise and cut out core. Reserve half the pineapple for another use. Cut each remaining quarter into 4 lengthwise slices, then cut each slice in half crosswise to make 16 thin wedges. Skewer each lengthwise.
In a small saucepan, combine sugar with 1/2 cup water. Bring to a boil, swirling to dissolve sugar; boil, swirling occasionally (do not stir), just until golden and honeylike. Remove from heat and slowly whisk in coconut milk (mixture will bubble furiously).
Heat a grill to high (450° to 550°). Using a pastry brush, coat pineapple pieces with caramel sauce. Grill just until marks appear, then turn to mark other side, 4 to 5 minutes total. Put skewers on a platter, sprinkle with toasted coconut, and serve with remaining caramel sauce for dunking.