Ah, I think I only used an existing skybox for Old Lykaon. Yes, you can easily change the speed. Don't take everything I am going to say for granted, since I can only work from my memory (W3 skies are completely different and way more awesome. Seriously

!!!).
Open the dynamic_clouds skybox. In its properties, there should be two materials. One of them should have information about the speed, the used texture, etc. in its node properties. Then you can simply experiment what you like.
My tip would be to use 2 or more skyboxes with different clouds and alpha channels (so you can only see clouds, no sky texture) and let them have different speeds. Looks very nice in real time (unlike in the video, where you can see that it is an actual skybox).
In the video I still used a texture for the sky itself, but I got rid of that now, so I can actually change the colour of the sky in the area environment properties. This way you have the most control over what happens up there.
http://forums.cdprojektred.com/threads/25831-Lykaon?p=1370691&viewfull=1#post1370691