Warm 1/2 Tbsp. oil in a small skillet over medium heat. Add onion, celery and garlic and cook, stirring, for 3 minutes. Set aside and let cool.
Combine remaining ingredients, other than remaining oil, in a medium bowl. Stir in onion mixture. Cover and chill for 30 minutes.
Warm remaining 2 Tbsp. oil in a heavy skillet over medium-low heat. Make 4 cakes out of crab mixture. Add to pan and cook until golden, 4 minutes. Flip and cook until golden and crisp, 3 minutes. Cover and cook on low for 1 minute to warm through. Serve with lemon wedges and green hot sauce, if desired.