In a large bowl, combine salmon, shallots, ginger, egg, crushed red pepper, 1 teaspoon salt, and 1/4 teaspoon ground pepper. Form mixture into eight 1-inch-thick patties, packing each firmly; transfer to a plate. Place in freezer until just firm, about 20 minutes.
Heat a large nonstick skillet over medium-high heat. Add salmon patties; cook until browned on both sides and just opaque throughout, 4 to 6 minutes per side, turning carefully. Serve with lime wedges and Sesame Mayonnaise, if desired.
To make Sesame Mayonnaise: In a small bowl, stir together mayonnaise, scallions, lime juice, and sesame oil. Chill until ready to serve.
Wrap the patties individually, and freeze up to two months; thaw before cooking.