Place the potatoes in a medium saucepan. Add enough cold water to cover and bring to a boil.
Add 1 teaspoon salt, reduce heat, and simmer until tender, 15 to 18 minutes. Drain and run under cold water to cool. Cut into quarters.
Meanwhile, heat 1 tablespoon of the oil in a large nonstick skillet over medium-high heat.
Season the salmon with ½ teaspoon salt and ¼ teaspoon pepper. Cook until opaque throughout, 4 to 5 minutes per side.
In a large bowl, combine the horseradish, vinegar, scallions, remaining 3 tablespoons oil, ¼ teaspoon salt, and ¼ teaspoon pepper.
Add the potatoes and watercress to the dressing and toss to combine. Serve the salad with the salmon.