No, you really just want to use inline CSS. Is it really worth all of the trouble just to cache 3 kilobytes of data (probably 20 milliseconds of download time)?
That is what I said, yes, except that I wanted a tool that does the inlining. But as another comment said, that tool would probably not worth the hassle, too.
I'm not totally sure what you mean by tool. Whatever framework you're using surely can include an external file, and if not, even Apache itself can handle this via SSI. It really depends what your web app looks like.