I remember vaguely from my Electromagnetic fields class (which was a long time ago) that this effect didn't amount to much at audio frequencies. So I tried to find some documentation corroborating that, and here's the result:

http://ecee.colorado.edu/~ecen3400/Chapter%2020%20-%20The%20Skin%20Effect.pdfLook at table 20.1 on page 4. For copper, at 1000 Hz, the skin depth is still 2.1mm. That's right around 12AWG, like your house wiring.

I'm going to wave my hands a little on the math, and since the skin depth is inversely proportional to the square root of frequency (for a given material, permeability and conductivity are constant), that going up to 4kHZ (4x the frequency) will give you half the skin depth (1/sqrt(4)), or about 1 mm, which is still 18 AWG wire. Double again to 8kHZ, 0.5mm is 24 AWG.

So for me, I'm pretty convinced skin effect is not a thing at audio frequencies.