Have an install.pl that copies it to the hard drive and executes it from there?

What about creating a dynamic ramdrive and copying the script into there?

Can you somehow bootstrap the code into a browser, and launch it from there, so it sits in the cache and namespace of the browser session? Something like "Read the docs in your browser, click here to demo the app".

There's no way to "cache" the script yourself, through your perl code, other than to do something like the solutions above. You're dealing with a mechanical limitation (the cdrom spindown), and that's not something you can modify or adjust with your perl code. Work around it.