To prepare dressing, combine first 7 ingredients in a blender; process until smooth.
To prepare salad, bring 4 cups water to a boil in a large saucepan. Add shrimp; cook 1 minute. Add celery; cook 1 minute. Drain and rinse with cold water; pat dry.
Place shrimp mixture, arugula, grapes, and basil in a large bowl. Drizzle with dressing; toss gently to coat. Top with cheese and walnuts.