Granted, I'm suggesting something else than CGI::Application about which I know little. I do not know the scope or size of what you already have running, so YMMV.
You could look into HTML::Mason and its concept of dhandlers and autohandlers.
Using a dhandler, you can use the URLs of the form you indicated, while passing parameters with those URLs to a single script/component. For example: a URL of the form http://example.com/archives/753/pdf only requires a suitable dhandler in /archives/ that obtains the document with ID 753 and displays the PDF file stored for it.
Update: Added simple day-to-day example