Combine first 4 ingredients in a bowl; gently fold in crab.
Heat a large cast-iron skillet over medium-high. Coat pan with cooking spray. Place avocado halves, cut sides down, in pan; cook 2 minutes or until lightly browned.
Place avocado halves, cut sides down, on a cutting board; cut a very small (1/16-inch) slice from the bottom of each half so that it stands flat. Turn over; spoon about 1/2 cup crab mixture into each avocado half.