Drain salmon, remove and discard bones and skin, and place meat in a bowl; mash with a fork. Add celery, mayonnaise and 2 Tbsp. bread crumbs. Finely chop the green portions of the scallions and add half to salmon; mix salmon until all ingredients are incorporated.
Place remaining 3/4 cup plus 2 Tbsp. bread crumbs in a shallow bowl. Add remaining scallion greens and thyme, then toss to combine. In another shallow bowl, beat eggs well.
Form salmon mixture into 8 patties about 2/3-inch thick. Working one at a time, coat patties in bread crumbs, turn in beaten egg, then coat in bread crumbs again. Place on a plate.
Heat oil in a large nonstick skillet over medium heat. When hot, add 4 patties and cook for 3 minutes; flip with a spatula and cook until crisp on both sides and heated through, about 3 minutes more; keep warm. Repeat with remaining cakes. Serve hot with lemon wedges.