You could create a folder somewhere like /Data/Sites/1/commoncss
put most of your css files there along with any images they reference. In the skin folder you must still include the style.config, layout.master, theme.skin, favicon.ico and IESpecific css files, but the rest of your css could go into the common folder then configure the paths in style.config as discussed in the article.
The style.config would be the same in both of your skins but each would need its own copy.
Hope it helps,
Joe