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][1]; 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, 


  [1]: http://aviation.stackexchange.com/questions/25089/why-is-the-coefficient-of-drag-for-straight-wings-at-supersonic-speeds-lower-tha