To make the marinade, whisk the skyr, curry powder, ginger, garlic, olive oil, lemon juice, cilantro, and salt together in a bowl or shallow dish. Add the shrimp and toss to combine. Marinate 10-20 minutes.
Meanwhile, make the sauce by stirring the skyr and mango chutney together in a small bowl.
When ready to grill, heat a grill pan over medium high heat. Thread the shrimp onto metal or wooden skewers (about 3 shrimp per skewer). Grill the kebabs 2-3 minutes on each side until shrimp are cooked through. Serve with mango dipping sauce and lemon wedges on the side.