What you need is a A2DP headset, that's one that can send the Media audio (stereo) over BT. One such is the Jawbone Icon but a lot of the car handsfree gadgets use it too. I just verified this after updating the firmware on the Headset (which b.t.w. is not a stereo headset but a BT earpiece but has A2DP capability if updated).
You pair it and it should work. Test by opening a random youtube clip on the phone. If it works with youtube, it works with Skype. If you still get no sound open your BT settings and hold down on the row that represents your paired headset until a settings window is displayed, go to settings at the bottom and see if "Media Audio" is checked, if not check and try again. Should work now.