Cut red snapper into 1 1/2-inch strips. Place in nonaluminum bowl. Add lime juice and orange juice; toss gently. Cover and refrigerate 2 to 3 hours or until fish is completely opaque. Drain and discard liquid.
Combine red snapper with plum tomatoes through ground pepper; toss gently. Cover and chill 1 hour. Serve in radicchio-lined compotes. Garnish each serving with lemon wedges.