Heat oil in a large skillet on medium. Halve 1 lemon and place halves, cut sides down, in the skillet. Season salmon with ½ tsp each salt and pepper and cook until golden brown and opaque throughout, 3 to 6 minutes per side. Transfer salmon fillets to plates. Transfer lemon halves to a cutting board and cut each in half.
Meanwhile, in a large bowl, toss cucumbers with ¼ tsp salt. Finely grate zest of remaining lemon into a food processor and squeeze in 3 Tbsp juice. Add feta and yogurt and puree until smooth.
Toss with cucumbers to coat, then fold in mint and freshly cracked pepper. Serve with salmon and a charred lemon wedge for squeezing.
