Cook rice according to package directions. Meanwhile, prepare a charcoal or gas grill for high heat (450° to 550°; you can hold your hand 5 in. above cooking grate only 2 to 4 seconds). In a medium bowl, combine cucumber, vinegar, soy sauce, sugar, jalapeño, and onions. Set aside.
In another medium bowl, combine oils with shrimp. Skewer shrimp lengthwise through the tail so they're straight. Grill, turning once, until cooked through and grill marks appear, about 4 minutes total. Sprinkle with sesame seeds and serve with rice and cucumber salad.
Note: Nutritional analysis is per serving.