That’s a clever solution, but you’re an idiot for trying it when there are simpler and more obvious solutions. Just put an HTTP daemon on that other server, point a domain at it, and link to the files there.
I need to run back-end code when the download link is clicked. Does this solution still hold?
Unless the action is idempotent, it shouldn’t be a link. It should be a button in a form instead. The form can POST to your main server which can do whatever work is required and then send back a 302 response to redirect the user to the file on the other server. You probably don’t want search engines clicking on it and triggering whatever work you are doing on the server; using a form prevents that.