I want to just click (or double click) the Audio CD icon on the Xfce desktop to play the CD. How do I do it?

I've been able to make the CD play automatically when inserted by checking "play audio CD's when inserted'
in the removable drives and media settings, but I can't find a way to make the CD start playing when I double click its icon!
It just opens the CD in a file manager, shows the location as "cdda://sr0/" (the cd device) and lists one file as "/Track1.wav"

Interestingly enough, this file opens the Movie Player when double clicked which doesn't know how to handle it.
When I try to open it with Parole, it complains it needs a plugin to play audio cd's, even though when started as parole --device=cdda://sr0/,
it plays the cd just fine.
It can be, however, opened with Audacious which plays it as "Track 1" by artist named ".gvfs" with album title "cdda mount on sr0".

I am providing this extra information just to give some extra clues as to what is going on here!

Any help is much appreciated!