Cut up avocados and place them directly into a food processor. Puree with hot sauce and salt until smooth. Heatgrill to medium-high heat.
In a bowl, rub shrimp with oil, garlic and cayenne. Thread 3 shrimp onto each of 8 skewers, leaving small spaces between shrimp. (If using wooden skewers, soak in water for 1 hour before using so they won't burn.)
Grill shrimp covered, about 2 1/2 minutes per side, until golden and just cooked through. Serve with avocado dip.