Using a vegetable peeler, peel ribbons along the length of each cucumber half. Peel the cucumbers until you reach the center where the seeds are and discard the core. In a bowl, toss your cucumber ribbons with ½ tsp of salt.
In a large skillet over medium-high heat, melt your butter and 1 tbsp of oil. Seasons your fish with ½ tsp of salt and ¼ tsp of pepper. Place your salmon in the skillet, skin side up, and cook for 10 minutes, turning halfway through. Cook until the fish is golden brown and cooked through. Remove from the skillet and cover with tin foil.
Clean your skillet with a paper towel to soak up the oil and add 1 ½ tbsp. Heat your oil over medium-high heat until the oil begins to simmer. Add your cucumber to the skillet and sprinkle the remaining ¼ tsp of pepper and your stevia into the skillet.
Cook your cucumber ribbons for 2 minutes, or until the cucumber is warmed through. Stir in your vinegar and divide your cucumbers onto your plates and top with a salmon filet.