I drill the holes in the wings, too. I use as thin drill bit as possible (0.3mm or 0.25mm). And try to keep the holes as close to the strut socket as possible. I use elastic thread for rigging, I glue (gel CA) one end to the shallow hole in the lower wing. Then I attach the upper wing with pre-drilled see-through holes. When set, I pass the threads through the holes in the upper wing. A blob of gel CA glue applied to a loose line under the wing to the spot where it enters the hole, makes it fixed when it is tightened upwards. When set, I cut the excess threads flush with the upper wing surface using a fresh razor blade. Then I fill the holes with dense paint, sand flush using very fine sand paper. Then I paint the upper side of the upper wing.
Hope that makes sense.
As for the model which is already built, it maybe problematic to drill the holes

Me, I would not dare do it. But maybe you are not afraid to loose the upper wing and repeat the assembly with the rigging.
Some time ago, at a modelling competition, I have seen a modeller who rigged 72nd scale models without any holes. He just glued the elastic thread to the bases of struts when the wing cellule was assembled. I have tried it but it was hard to tighten the line, pressing it home with a needle and not to glue the thread to the needle instead of glueing it to its destination. An it always led to some glue marks on the wing and the struts. That is why I prefer the method with the holes, even though it requires making up that mess on the upper surface. If you check my build logs in 72nd scale you will find some photos of the process, for instance here:
http://forum.ww1aircraftmodels.com/index.php?topic=1799.50I have some more, if you are interested.