Place 1 tbsp (15 mL) lime juice, avocado, stock, sour cream, sugar, cumin and cayenne in food processor or blender and pulse until smooth; season with ¼ tsp each salt and pepper. Transfer to a small saucepan. Set aside.
In a bowl, toss shrimp with olive oil and season with remaining salt and pepper. Grill shrimp on medium-high heat, 1 to 2 min. per side, or until just cooked through. Cut lime into thick wedges and grill to lightly mark.
Bring reserved avocado sauce to a simmer over medium-low heat. (Set saucepan on barbecue stove burner, if available. Otherwise, use a stove burner.) Divide shrimp evenly among 4 plates, and serve with the warm sauce and grilled lime wedges.