Salmon: Put a grill pan over medium-high heat or preheat a gas or charcoal grill. Drizzle the salmon with olive oil and season with salt and pepper, to taste. Grill until the flesh is cooked through and flakes easily with a fork, about 6 to 8 minutes on each side. Set aside to cool for 20 minutes.
Patties: Using a fork, flake the salmon into 1/2-inch pieces and put into a medium bowl. Add the egg, chives, 1/2 of the crushed crackers, the corn, mustard, mayonnaise, capers, lemon juice, and lemon zest. Mix gently until just combined. Form the mixture into 2 1/2-inch diameter patties, about 3/4 inches thick. (If the mixture is too dry to form into patties, add extra mayonnaise, 1 tablespoon at a time,) Carefully coat the patties in the remaining crushed crackers and refrigerate for 1 hour. In a large nonstick skillet, heat the oil and butter over medium heat. Add the patties and cook until golden and crispy, about 7 to 8 minutes each side. Drain on paper towels.
Sauce: In a small bowl, mix together the yogurt, capers, lemon juice, and lemon zest. Season with salt and pepper, to taste.
Arrange the salmon cakes on a platter and serve alongside the sauce.
The salmon can also be baked in a 350 degree F oven. Drizzle the salmon with olive oil and season with salt and pepper, to taste. Put in a baking dish and bake until just cooked through, about 15 to 20 minutes