What would happen if the wing of a supersonic plane goes into the shock wave from the nose?
Not much.

The outer wing would fly in undisturbed flow and an inboard wedge would fly inside of the Mach cone of the nose. This is similar to a wing with a supersonic leading edge; something that has been quite common with Mach 2+ designs before swing-wing aircraft. The nose shock of a pointed nose is a weak, oblique shock which does not alter flow parameters dramatically,