In a medium pot, bring potatoes to a boil in salted water over medium-high. Reduce heat and simmer until potatoes are tender when pierced with a knife, about 12 minutes. Drain and rinse under cold water. Alternately thread potatoes, corn, andouille, and shrimp onto four 8-inch skewers.
Heat a grill to medium-high. Clean and lightly oil hot grill. In a small bowl, combine butter, hot-pepper sauce, and Old Bay Seasoning. Grill kebabs, turning and brushing with butter mixture occasionally, until shrimp are opaque throughout and corn is tender and beginning to char, about 8 minutes. Serve with lemon wedges.
Soak wooden skewers in hot water for 15 minutes before grilling, or use metal ones. No grill? Broil on second highest rack using metal skewers. Cooking times are the same.