In a large skillet, saute zucchini and onion in 1 teaspoon oil until tender. In a small bowl, combine the egg, bread crumbs, mustard, thyme, cayenne and zucchini mixture. Fold in crab. Refrigerate for at least 30 minutes.
With floured hands, shape mixture into four 3/4-in.-thick patties. In the same skillet, cook crab cakes in remaining oil over medium heat for 3-4 minutes on each side or until golden brown.