Place 3 tortillas on a work surface. Divide cheese and hot dog slices evenly among tortillas. Sprinkle each portion with 1 tsp. chives, a large pinch chili powder and a pinch ground cumin. Top each with remaining tortillas.
In a medium skillet, heat 1 tsp. oil over medium heat. Put 1 quesadilla in pan, then rest a small plate on quesadilla to weigh it down; cook for about 2 minutes, until golden underneath. Remove plate, flip quesadilla with a spatula, weigh down with plate and cook until cheese is melted and tortilla is crisp on other side, about 2 minutes. Keep warm. Repeat with remaining oil and quesadillas.
Cut each quesadilla with a pizza wheel or a large, sharp knife into 4 equal wedges. Serve wedges with salsa and sour cream.