You can specify HTTP headers for a path/location in nginx in a static website and have it include arbitrary headers. Most standards respecting browsers (like Firefox) accept HTTP header specified CSS like,

    #/etc/nginx/sites-enabled/whatever.conf 
    location /this-isnt-for-you.html { 
        add_header Link "<//site.com/isntforyouheader.css>; REL=stylesheet";
    }

    $ curl -I http://site.com/this-isnt-for-you.html
    curl -I site.com
    HTTP/1.1 200 OK
    Server: nginx
    Date: Mon, 28 Nov 2022 18:08:01 GMT
    Content-Type: text/html
    Connection: keep-alive
    Link: <//site.com/isntforyouheader.css>; REL=stylesheet
    ...

This works to set CSS atributes only for a specific URL on my static websites using .html files. For nginx. But nginx is a very common and secure choice for static sites and available in everyone's repos. And you can probably add arbitrary headers per path with other static webservers configs too.

if it's served via a CDN then it may be possible there, they often have facilities to transform the content based on headers etc