I managed to merge my Skype and Xbox Live accounts, and couldn't get them separated again.

The steps I found to unlink within the XBox UI didn't work, futher research now leads me to the following discussion which I am about to try: https://answers.microsoft.com/en-us/outlook_com/forum/oemail...

Edit: it looks like this was possible in the past (basically deleting the Skype account?), but not anymore.