Depends on what your "Dwarf Korean Pine" is. The ones I've seen have actually been P. pumila misidentified, but I don't know if that applies to all of them or not. Obviously, if they are more P. pumila, then they'll cross freely with other P. pumila.

True P. koraiensis doesn't cross easily with P. pumila though; seed yield from cross-pollination between them would be very low.

Resin

If they are dwarves in reality as well as in name, they will produce very few cones on their little crowns. And if either is the only one of its species, it will self-pollinate, which means very few filled seed per cone, if any. Plus, it will take many years before even those few cones are borne on your treelets, so you may be better off buying cheap Chinese pine nuts, which are actually from Korean stone pine (P. koraiensis), and press the oil from them.