Bring a large pot of water to a boil. Add sugar snap peas, asparagus, and green peas; cook 2 minutes. Drain and rinse with cold water until vegetables are cool; drain well.
Meanwhile, heat a large nonstick skillet over medium-high. Pat fish dry with paper towels; sprinkle flesh side of fish evenly with 1/2 teaspoon salt and 1/4 teaspoon pepper. Add 1 tablespoon oil to pan; swirl to coat. Add fish to pan, skin side down. Cook until skin is crispy, 5 to 6 minutes. Turn fish over; cook until desired degree of doneness, about 2 to 3 minutes.
While fish cooks, whisk together shallots, mustard, lemon zest, lemon juice, and remaining 1/2 teaspoon salt and 1/2 teaspoon pepper in a large bowl. Gradually add remaining 2 tablespoons oil, whisking constantly. Add blanched vegetables, arugula, and mint; toss gently to coat. Serve salad with fish.