Does wire running up an exterior wall require conduit?
A UV resistant type of non metallic called UF (underground feeder) is allowed to be used exposed code requires the cable to be protected , above 8’ is normally considered protected by height in the national electric code. If the cable height is above 8’ it could be routed along the siding but would look like a diy hack job. Since conduit would be required for the rise to 8’ why not do the run in conduit or pull the line inside in the wall along the roof truss to the soffit and out, that would be the pro way to do it and you may have a receptacle you can tap closer, a few small holes in the drywall to patch , this would be my suggestion. 

Note low voltage is not restricted as much as power.