If you can't remove the cooler or any other heavy items attached to mobo (gpu), then you NEED to pack the inside tight. Use some styrofoam or some type of heavy foam with little give and then cut it out so that it braces against the case walls and holds your cooler/gpu's in place. Really you want as little give as possible, because we have to expect the worst here, a drop from 1-3ft from any angle is possible and it could happen several times during a trip.
Biggest key to shipping breakables is to package tightly and also have a good buffer zone between items. On smaller boxed items what can really get you is not enough packing inside, where the item bounces around back and forth inside the box (same idea for items inside a pc case). Your idea for using the factory box + another box and peanuts is probably fine, just make sure the peanuts are solid so the factory box can't move around a lot inside.