Lightly brush 1 side of each won ton skin with oil. Center each square, oiled side down, on a muffin cup (1 1/4-in. across bottom). Gently press skin down to line cup smoothly; skin will extend above pan rim.
In a 6- to 8-inch frying pan over medium-high heat, stir 1/2 teaspoon oil and onions until onions are limp, about 1 minute. Remove from heat. Stir in chilies, crab, and mustard-mayonnaise.
Fill each won ton cup equally with crab mixture. Sprinkle filling evenly with cheese.
Bake in a 350° oven until rims of won ton skins are golden and crisp, 8 to 10 minutes (7 to 9 minutes in a convection oven). Lift from pan and serve hot.