|You shouldn't need to configure anything on your WebAPI to make it work externally vs Internally.
If the endpoint your trying to hit works from the local lan, then it should work from any source that hit's the correct API, if your getting a 404 AND your sure the traffic is getting from the outside to the inside and actually hitting your web API then it's because the routing in the dotnet app is not working.
If the traffic is getting to the internal IP, but NOT being redirected to the WebAPI, then the problem is with your forwarding server, most likely the server is trying to handle the request instead of proxying it out to the required destination.
The FIRST thing to check is the log files for your proxy forwarder, if your using Nginx then these should normally be in something like /var/log/nginx on a linux server (Can't help if it's winyhoos sorry), you should try "tail -f <logfilename>" in an ssh window while you throw a request at the IP so you can see it in real time.
If the access log shows activity, then you don't have your proxy forward configured correctly, but you don't have any config errors either.
If the error log shows activity, then you have a configuration error and the error log should tell you what to do.
My gut feeling from your description is that your going to see activity on your access log, not on your error log....
But I'll leave that until your reply....