Authentication in email forwarding between SMTP servers

Question

I am writing a Mail Relay Server in PHP for Newsletter mailings. This server encodes all links in the e-mails so that they point to an accompanying website for tracking (click count only) and redirecting.

This Mail Relay Server will run as a service for multiple customers sending Newsletters. Each customer has it's own credentials for the Mail Relay Server. The newsletters may go to a great amount of recipients.

As of this, I can't forward all mails through my own mail account (would bring my webhoster on the blacklist). This is why I thought of forwarding them to the recipients' mail server myself, using the techniques used in e-mail forwarding all around the world.

My question now is: Is there a way to forward e-mails from an own SMTP server to another, for which I don't have a mail account and cannot send credentials?

Thanks in advance for any help and clarification on this.