What you need to do is make lots of seperate bitmaps using the print screen function when you're running the viewer and have made a change to the skin.
Then you should batch convert them to the size you want to use and create an avi/animated gif from them using either something like Adobe Premiere/Sony Vegas or Macromedia Fireworks.
There are programs that allow you to record such things, I've seen many graphics tutorials done this way, in fact I have several hours of 3DS Max tutes that are recorded in real time. I can't recall the names of the programs that do this though, but I know they exist.
I use camtasia studio for this job.. creates some good quality AVI files of small size too, for example, I created a quick vid to show moving tree polys around on a track for a friend who was updating an old N2K3 sandbox track in 3DS and doesn't really know 3DS... full screen (1280x1024) came to under 2Mb
camtasia's not free however but not overly expensive if you're (semi) serious about this sort of thing.