Kijanki: it is a true statement that signals attenuate within a conductor as you get farther away from the surface of the conductor into the interior. I didn't mean to suggest that skin effect doesn't at frequencies below microwave but that it is at higher frequencies where it becomes a bigger deal.
You mentioned skin effect as being significant with video signals. Video signals operate in the MHz range, which is below what is typically considered the microwave frequency range. I do agree with your suggestion that skin effect can be significant for frequencies in the MHz range. At video frequencies the skin depth is very thin, so the silver plating can be economically applied at thicknesses greater than the skin depth. Silver plating is a less effective cost-saving strategy for audio frequencies because the skin depths at audio frequencies are much larger.
There is a relevant figure of merit called the 1% depth of penetration. The 1% depth figure indicates that point at which the signal magnitude is about 1% of it's surface value. It is about 4.6 times the skin depth.
In general, skin effect is significant when the skin depth is small compared to the size of the conductor. At audio frequencies, the skin depth is going to be on the order of 20 mils, so I would think that for significant skin effect, you're probably looking at conductors that are on the order of at least 0.1 inch. That would be more like AWG 10.
There are other effects that are significant when thinking about signal propagation through a conductor (you had me going to my old textbooks to look this stuff up). For example, as the magnitude of the signal decreases the relative phase of the signal also changes. I believe that at the skin depth, the signal is about 180 degrees out of phase with respect to the signal at the surface. Also, when you have multiple conductors, there are proximity effects where the electromagnetic fields of the conductors interact and can effectively reduce the skin depth. Skin effect also increases the impedance of the conductor to signal propagation, although I am unfamiliar with the formula that was cited in the web link that you posted (I took a look at it and it looks to be a pretty good link). However, the skin depth calculator is correct, so I will assume that the AC/DC resistance ratio presented is correct as well.
Is any of this stuff audible, significant or even detectable at audio frequencies? It's impossible for me to say without data, so I tend to not tell people that they aren't hearing what they say they are hearing. I question how significant this stuff is at audio frequencies and because of the amount of hyperbole that has so come to characterize the audio biz, I am skeptical of claims that rely upon nothing but buzzwords. The thing is, if I spent big money on cables, I would have a vested interest in convincing myself that there really is a big difference because I would have a commitment to feeling that I haven't wasted my money. It would be nice to see some real data on this stuff. In my mind, it would make all this talk of "focus" and the like, a lot more credible. As I stated, the amount of hype and questionable "audiophile reviews" just hurts the credibility of the industry in my mind.