The WordPress Codex function you want is wp_login_form. What you could do is create a simple one-off PHP file that includes the WordPress API file (wp-blog-header.php) and calls the function. Set the redirect URL of the wp_login_form function to be your Perl code that provides files. Or perhaps create some mishmash where your Perl code is doing the interface generation and you use something like LWP::Simple to scrape the information into a Perl string.

To be honest, I would create a custom script completely in PHP to do what you're trying to do. You could perhaps delve into the WordPress API to create a plugin that allows users to see the files you're trying to deliver. Perl, for all its power, is sometimes not the right tool for the job.