Bring a large pot of salted water to a boil. Add the carrots and cabbage and cook until tender, 6 to 7 minutes. Drain and return to the pot. Add the butter and stir until melted; season with salt and pepper. Cover to keep warm and set aside. Meanwhile, mix the sour cream, mustard and vinegar in a small bowl; set aside.
Heat the vegetable oil in a large nonstick skillet over medium-high heat. Season the salmon with 1/2 teaspoon salt and a few grinds of pepper; add to the skillet, skin-side down, and cook until the skin is golden brown and crisp, about 4 minutes. Flip and cook until just cooked through, 1 to 2 more minutes.
Stir the dill into the vegetable mixture. Serve with the salmon, mustard sour cream and lemon wedges.