There are situations where uncommon things like this are neccessary.
You'll loose a great amount of IMAP-features like folders and server-stored postbox, but many mailservers and clients don't use them anyway.
At first, you should look at CPAN (www.cpan.org) for POP3 and IMAP modules.

Net::Server::POP3 seems to be a good choice. You could define subs for each POP3 action and the whole protocol is done by the module.

Net::IMAP::simple is a good choice for the client side. It offers only few IMAP-commands, but all you need is list, read and delete mails and this should be easy as this module is well documentated and there are good samples.

You won't get the source for the whole proxy server here, but the modules are a good way to start and feel free to come back if you got any questions.

PS: I think this script would be a nice sample for the Cool uses for Perl section on this site.