Thanks for the reply, I believe the effect i'm describing is something very different from the skin effect, it works in DC and shouldn't change resistivity of the core/skin of a wire. I think i made the example too complex by using a conducting wire.
Imagine an electron gun firing a line of continuous current in a vacuum. Is the perpendicular electric field of the charged beam stronger than a corresponding stationary beam? I believe it is, based on numerical integration of time retarded electric fields produced from a beam of moving charges. But I'm often wrong, hence there will probably be some reason why these models are wrong?