We utilize a global CSS file to control styles for some elements that are common to all of the pages. We want to be able to update the global CSS file name without having to redeploy all of the pages.
I am doing something similar.
I have a very basic component that includes a DCR that is just a textarea.
The contents of this are the link to the CSS file.
We dont change the file name as such but do add a parameter to the end for cache busting purposes.
You can put an include file in the head section of the page, and have the call to the stylesheets (and any other scripts) in the include file. That way you only have to change the link within the include file, publish it out and it will apply to the entire site. Note you will need to have server side includes enabled on your site. e.g.
page content:<html>
<head>
<!--#include virtual="/includes/head_code.htm" -->
</head>
<body>
<p>Page text</p>
</body>
</html>head_code.htm<link rel="stylesheet" href="/includes/stylesheet.css" /><script src="/includes/scripts.js" type="text/javascript"></script>