Preheat the oven to 400 degrees F. Mix the salmon, corn, egg, 3 tablespoons each breadcrumbs and tartar sauce, the roasted red peppers, parsley, lemon zest and 3/4 teaspoon Old Bay in a large bowl. Gently form into eight 3/4-inch-thick patties and freeze until just firm, about 5 minutes.
Meanwhile, make the dressing: Whisk the remaining 2 tablespoons tartar sauce, the lemon juice, 1 tablespoon water, the remaining 1/4 teaspoon Old Bay, and black pepper to taste in a large bowl.
Put the remaining 5 tablespoons breadcrumbs in a shallow bowl. Press the salmon cakes in the breadcrumbs to coat both sides. Heat the oil in a large ovenproof nonstick skillet over medium-high heat. Add the salmon cakes and cook until golden brown, 3 to 4 minutes per side. Transfer the skillet to the oven and bake until the cakes are heated through, 6 to 8 more minutes.
Add the greens to the bowl with the dressing and toss. Serve the salmon cakes with the salad, more tartar sauce if using, and lemon wedges.