I agree that this is certainly the case for higher audio frequencies but at lower frequencies, the current flows well within the conductor. The skin depth at 100Hz for example is somewhere around a quarter inch.
I had direct experience with multiple, non-audio installations where cable conductors were turning green, smelling bad and becoming brittle. The problem was eventually traced to fungus attacking the PVC jacket. You should seek out an insulation that is known to be structured in a way that is fungus resistant or has additives to prevent microbial growth.
