Welcome, kopiersperre.
PVD doesn't actually "play" anything. It only asks Windows to "open" the file(s) recorded in the File Path field. Windows uses the application associated with the file type to do so. So the easiest answer to your question is to create an Internet Shortcut for the stream, and record that in the File Path field. Add .url to the list of supported file extensions at Preferences>File Scanner. Play will then launch the stream in your default browser.
An Internet Shortcut is a text file with a URL extension of the form:
[InternetShortcut]
URL=http://...
To launch the stream in a particular player, you would have to save the URL as a playlist of a type associated with that player. See your player's documentation to determine if that's possible, and if so, how.