Hello there,
We can make an application that we will place on your server, and will connect it to your mail server. So, when it will receive an email, it will update the link your subdomain will load on a page. We can create an iframe on your subdomain, and link sent to email will be displayed on that iframe, it will auto-refresh the iframe URL so, it be updated with new email links.
Let's discuss to plan this out in great way to have it work efficiently.
Talk soon, Thanks.