Combine egg and next 7 ingredients in a large bowl. Fold in crabmeat. Shape mixture into 18 (1 1/2-inch) cakes.
Heat 1 tablespoon butter and 1 tablespoon olive oil in a large nonstick skillet over medium-high heat. Sauté half of patties 1 to 2 minutes on each side until golden brown. Repeat with remaining butter, oil, and patties. Serve with Cucumber Relish.