Heat the oil in a 12-inch nonstick skillet over medium-high heat. Add the potatoes, onion, bell pepper, 1 tsp. salt, and 1/4 tsp. pepper and cook, stirring often, until golden-brown, about 10 minutes. Reduce the heat to medium and continue cooking until the potatoes are tender, about 15 minutes more; season to taste with salt and pepper.
Meanwhile, combine the sour cream, 1 Tbs. of the chives, 1/2 Tbs. of the lemon juice, the mustard, 1/2 tsp. salt, and 1/8 tsp. pepper in a medium bowl and stir well; set aside.
When the potatoes are tender, gently fold in the salmon and the remaining 1 Tbs. lemon juice and continue cooking until heated through, about 2 minutes more. Transfer the hash to plates. Garnish with the remaining 1 Tbs. chives and serve with a dollop of the chive sour cream.