I have deployed a website on Webfaction using Flask app for the site's main functionality and an AWStats app for analysis. The path for this AWStats app is /stats, but if I try to access my stats, Flask takes over and renders a 404-error page.
How do I exclude this /stats-path?
You're approaching the problem from the wrong end.
When you access the somesite/stats path you're asking a webserver and then an application server. Or at least this should be in a deployed environment.
It's the webserver that manages the routing. So there are plenty of ways to do this in your webserver configuration.
For example a <Location /stats> section in Apache or a location /stats {} directive in NGINX.
