Sorry for the potentially ridiculous question.
Is there some sort of hack or work-around to upgrade OWA to 2007 while using Exchange 2003? If not, are there any ways to improve the default layout / skin? Maybe Greasemonkey scripts?
No, you can't do that.
You would probably be better served asking over at StackOverflow as far as reskinning OWA as it really is an asp programming question, not a Server admin question.