OK. Now I will have to fiddle some more with skins, because I've found that I didn't give some a fair shake.
Here's what fooled me: when you change skins, it doesn't happen right away. Instead, the SL client passes through an intermediate stage where the new skin and the old skin are superimposed on one another, out of focus. During that time, you look like I imagine a corpse that has been floating out in the water for a while must look. (Quick! Get Jerry Bruckheimer to do an episode of CSI in SL!)
(No, I won't include a picture of it!)
On earlier attempts to change skins, I anxiously zoomed in on my face, eager to see my new look... and saw that! I always freaked out and immediately switched back.
This time, though, motivated much the same way I was when I finally bought a piano, i.e. by the voice in my head saying "You spent how much on that, and you're going to let it sit there?!", I bit the bullet and tried to stay calm, which I did. Mostly. Long enough to see the SL client settle in and fully render the new skin.
Thank goodness I did.
So, if you're reading this and haven't tried a new skin before, learn from my silliness. It'll be OK, really.