Thanks for the message on maintaining your emails. There is no way to delete the emails automatically after forwarding them, unless you setup a cron job. However, you can also delete the email account (for the forwarder)if you have a forwarder setup, then emails that are sent to the email account do not get saved, but they are automatically forwarded still. This is usually known as an email alias, but it works based on the principles of an email forwarder.
I hope this answers your question, if require further assistance, please let us know.
Am I correct in understanding that I don't need to create an actual e-mail account for the address I want to forward, then?