Combine 1 teaspoon oil and 1 cup carrot juice in a medium saucepan; bring to a boil. Gradually stir in couscous. Remove from heat. Cover and let stand 5 minutes.
While couscous stands, bring remaining carrot juice to a boil in a small saucepan; cook until reduced to 1/4 cup (about 2 1/2 minutes). Remove from heat; stir in 2 teaspoons oil, lime juice, jalapeño, ginger, and salt.
Fluff couscous with a fork; stir in 1/4 cup reduced carrot juice mixture and onions. Combine remaining carrot juice mixture, greens, and shrimp in a bowl, tossing gently to coat.