This is correct. Radio engineers have to allow for it. At audio frequencies it is negligible. Here's an analysis by Dr. Jim LeSurf, retired university physics lecturer and audio enthusiast.

http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/audio/skineffect/page1.html

He shows that the difference brought about by skin effect at audio frequencies is that some frequencies will arrive at the listener's ear 16 microns (micrometres) before the others. Can't see that making much audible difference.