In a bowl, mix shrimp, vinegar, tequila, liqueur, oil, jalapeño, garlic, green onions, cumin, and cayenne. Cover and chill 30 minutes or up to 1 day, mixing occasionally.
Meanwhile, cut peel and white membrane from orange. Working over a bowl to catch juice, cut between fruit and inner membranes to release segments into bowl. Squeeze juice from membranes into bowl; discard membranes and peel.
Pit, peel, and slice avocados; add to oranges and mix gently.
Drain shrimp, reserving marinade. Thread shrimp onto flat metal skewers. Lay skewered shrimp on a barbecue grill over very hot coals or very high heat on a gas grill (you can hold your hand at grill level only 1 to 2 seconds); close lid on gas grill. Cook shrimp, turning once and brushing frequently with marinade for the first 2 to 3 minutes, until bright pink and opaque but still moist-looking in center of thickest part (cut to test), 4 to 5 minutes total.
Mound salad mix equally on dinner plates. Push hot shrimp from skewers. Arrange shrimp, orange segments, and avocados equally on salad mix; moisten equally with chili-orange dressing, and add salt to taste.