Coat cold cooking grate of grill with cooking spray, and place on grill. Preheat grill to 350° to 400° (medium-high) heat. Brush hot dogs with 2 Tbsp. hoisin sauce.
Grill hot dogs, covered with grill lid, 6 to 8 minutes or to desired degree of doneness, turning occasionally. Grill buns, split sides down, covered with grill lid, 1 minute or until grill marks appear.
Grate ginger using the large holes of a box grater to equal 2 Tbsp. Squeeze juice from grated ginger into a medium bowl; discard solids. Add mayonnaise, next 3 ingredients, and remaining 2 Tbsp. hoisin sauce, stirring to combine. Add slaw, tossing to coat.
Serve grilled hot dogs in buns with slaw mixture and desired toppings.