Heat grill to high (about 450°) and put a grill pan on it. In a medium bowl, toss shrimp with garlic, salt, spices, orange juice, and oil.
Divide half of cheeses among tortillas, leaving half of each tortilla bare. Top cheese with zucchini, corn, and green onions. Top vegetables with remaining cheeses.
Oil grill pan, using tongs and a wad of oiled paper towels. Grill shrimp in pan, turning once, until just cooked through, about 3 minutes. Coarsely chop shrimp, scatter over cheese on tortillas, and fold tortillas to close.
Grill quesadillas on cooking grate, turning once with a wide spatula, until cheese melts and tortillas are golden, about 2 minutes per side.
Mix salad ingredients gently in a bowl and arrange on plates. Cut quesadillas into wedges and serve them alongside salad.
Note: Nutritional analysis is per serving.