Salmon Cakes with Lemon-Caper Yogurt Sauce

Salmon: 

• 1 pound skinless salmon fillet (see Cook's Note)
• Olive oil, for drizzling
• Kosher salt and freshly ground black pepper
• Kosher salt and freshly ground black pepper 

Patties:

• 1 large egg, beaten
• 1/3 cup (1/2-ounce) chopped fresh chives
• 26 saltine crackers, crushed, divided
• 1/2 cup frozen corn, thawed
• 2 tablespoons Dijon mustard
• 3 tablespoons mayonnaise, plus more, as needed
• 1 tablespoon capers, rinsed and drained
• 1 tablespoon lemon juice
• 1 tablespoon lemon zest
• 3 tablespoons vegetable oil
• 3 tablespoons unsalted butter, at room temperature

Sauce:

• 1/2 cup full-fat plain Greek yogurt
• 1 1/2 tablespoons capers, rinsed, drained and chopped
• 1 tablespoon lemon juice 
• 1 tablespoon lemon zest
• Kosher salt and freshly ground black pepper