You are totally on the wrong track here.
Electric field is zero inside a perfect conductor, never really true practically except in super-conductors and not the reason for electrons being on the periphery.
Current travels on the periphery only in AC current, not DC, reason being the penetration depth of EM waves in the conductor (EM wave associated with the AC current), I don't think putting it as electrons pushing each other away is right at all, its just that the associated wave travels well in air but decays as it enters the conductor(due to cutoff of the wave), and hence the associated current must decrease, as amplitude of EM wave and current are proportional. Its called the skin effect, you should look it up.
Electric field is zero inside a conductor(ideally) and the skin effect are two totally separate phenomenon.