Allowing users to send email via form from their own email address

If I wanted to set up a web form and use Universal Email to allow our users to email their own clients via that form using their own email address as the sending address, is this possible without our server very quickly being blacklisted for mail relaying? My understanding is that if mail was being sent through our server from many different domains, it could either be blocked completely or marked as spam.

The scenario is that we need to provide our users with a reminder email that they can send to their clients at specific times, but their clients should think that the email is coming from our users and not us. At the moment I have the form set up to send to our users from info@[ourdomain.com] so they receive the email but then have to forward it, which seems a bit clunky.