Blend the mayonnaise, egg, and lime juice in a large mixing bowl. Flake the cod into small pieces and add to the bowl. Mix in the celery and salt.
Pulse the bread in a blender or food processor to make fine crumbs. Pour the crumbs on a sheet of wax paper.
Tightly pack the cod mixture into 8 patties. Gently place each patty in the bread crumbs and turn to coat evenly. Heat the oil in a large, heavy skillet over medium heat. Place 4 fish cakes in the skillet and cook until the crumbs are golden brown, about 5 minutes per side; turn carefully. Repeat with the remaining fish cakes, adding more oil as necessary. Serve with chipotle cream.