Rewrite the script so it is not so likely to hang or at least returns a message that it could not complete.

If the script is likely to hang, it is also likely that your user's work is not completed. I doubt they will appreciate getting a message that says it is, when it isn't.

Mail::Sendmail is probably a good place to start. There are examples of how to use it there, and a Super Search here will almost certainly turn up others.