Modify sub domain, port and path of URL

First let me explain the reason for my question.
I am runnin an internet radio station country-radi eu and want to use ports 80 and 443 for streaming the audio, because in public networks ports like 8000 not open.
The problem also is, that for the standard URL country-radio the ports 80 and 443 are already used for the hompage and therefore not available for streaming.
So the streaming port has to be different, for example 8000.

My idea is, to use a sub domain for streaming. So instead www to use stream. For that I could create a new virtuell server for stream and send it to the real server www.
But the next step it would be necessary to change the port from 80 to 8000.
How can it achive it?
Would it also possible change the path too?

2. Case

I want to switch from an old sreaming server to a new one. For that I have to change the port and the path.
My idea was, to use "Anfrage-Umleitung" (requst transmit?).

But it doesn't work. The request always goes to port 8144 and to the path /sstream.mpeg and not to port 8044 and path /56.mp3.

What I am doing wrong?

Thanks for your help.