Soak skewers in water about 30 minutes. Preheat grill or grill pan to medium-high and brush with half the olive oil.
For the dipping sauce:
Whisk all ingredients in a small bowl until thoroughly combined. Set aside.
For the wedges:
In a large bowl, whisk curry powder, cayenne pepper, and the remaining 2 tablespoons of olive oil; season with salt and pepper to taste. Add sweet potato wedges and toss to coat.
Pierce 3 wedges onto each skewer and grill 4 to 5 minutes per side. Remove from heat and season with salt and pepper. Serve with cilantro yogurt sauce.