Can a supersonic plane use a subsonic wing if the nosecone shock produces subsonic airflow around the wing?
Normally, the flow speed at the wing is about the same as the speed ahead of the bow shock. Only if the fuselage is still conical and expanding at the wing station would the local flow speed be smaller. In order to be subsonic, you would need an absurdly blunt fuselage at Mach 1.5. But the wing is in a way still subsonic if its leading edge sweep is sufficient.

If you look closely enough, every shock has a subsonic region, but it is normally very small. The size of the subsonic region depends on the flow speed and the bluntness of the body causing the shock. See the diagram below for the parts of a classical oblique shock.


Diagram of an oblique shock and its three areas (picture source)

Supersonic aircraft are pointed at the front end in order to minimize the region of the strong shock, resulting effectively in an attached shock. The steeper the shock angle for a given flow speed, the higher the losses are. Only in hypersonic vehicles are blunt noses used on purpose, but nor for braking but for limiting local heat loads.

Why does the subsonic region disappear so soon? Because the cross section of the body stops to grow in flow direction, and the pressure energy past the strong shock is converted into speed again in expansion waves.

This means that the wings still fly in supersonic flow. If the fuselage has a constant cross section along the wing's chord, the flow speed is even the same as the speed ahead of the shock. Otherwise, the tail shock would have a smaller cone angle, which it does not have; the flow accelerates again in expansion waves when the conical nose changes to the regular fuselage, and again when the fuselage contracts at its end.

Now it makes sense to sweep the wing such that it will fit inside the Mach cone resulting from the inboard wing section. This results in a subsonic orthogonal speed component at the leading edge. The important insight here is that the spanwise speed component of the flow is not affected by the wing, and only the orthogonal component counts. If that component is subsonic, the whole wing behaves like a straight wing in subsonic flow. Note that all supersonic aircraft with a subsonic leading edge use blunt-nosed airfoils, because those create a suction force (PDF!) which reduces drag.

At higher speed sweep needs to be so steep that the problems of swept wings cannot be tolerated any more. Then and only then it makes sense to have a supersonic leading edge which has less sweep than the Mach cone and needs to be sharp in order to minimize drag. Another way to combine high sweep and good subsonic characteristics is to use variable sweep. This was the preferred solution until it was realised that high supersonic speed is rarely used in combat.