Pick out and discard any shells in crab meat. Grate 1 teaspoon of lemon zest and squeeze 2 tablespoons of juice; set aside.
In large bowl, beat together mayonnaise, egg, mustard, celery seed, onion powder, lemon juice, lemon zest, and hot sauce. Gently stir in crab meat, scallions, salt, pepper, and breadcrumbs. Form into 6 firm patties; refrigerate 30 minutes.
Heat grill to medium-high. Brush burgers with butter and grill 2 to 3 minutes per side. Meanwhile, lightly toast buns. Arrange arugula on bottom half of buns; top each with crab burger, 2 tablespoons chèvre, and remaining bun.