This thread reminded me my copy of Skype was years out of date so I downloaded the latest version of Skype, opened the .dmg, and drug the Skype icon/app to my /Applications folder. When I click on it Skype launches directly and there is no mounting of a disk image???
I know you are not a newbie, but it sounds as if there is something fubar in your Skype install. Have you considered starting over from scratch to see if the dmg opening can be eliminated?