In the oven, position a rack 4 inches from the broiler and heat the broiler to high.
Segment the oranges: Slice the ends off one of the oranges with a small, sharp knife. Stand the orange on one of its cut ends and slice off the skin in strips, cutting below the bitter white pith. Working over a small bowl, cut the orange segments free from the mambrane, letting each segment fall into the bowl as you go. Squeeze any remaining juice from the membranes into the bowl. Repeat with the other orange. Cut all of the orange segments in half crosswise and return them to the bowl. Add 2 Tbs. of the olive oil, 3/4 tsp. salt, the avocado, scallions, and lime juice to the oranges and toss gently to combine.
Combine the remaining 3 Tbs. of the oil, 1 tsp. salt, the paprika, cumin, and Tabasco in a medium bowl; stir well. Add the shrimp, tossing to coat. Arrange the shrimp on a foil-lined rimmed baking sheet. Broil until the shrimp are opaque and cooked through, about 4 minutes. Serve the shrimp with the salsa.