Hi there.
I don't know if this is the same issue as I was having, with two Skype icons.
I had one which was simply "Skype" and the other was ".Skype_Upgrade" which I couldn't get rid of.
I found this thread a few moments ago looking for answers myself and considered what was mentioned here, so I removed Skype from Applications, placing it into trash, then I emptied trash, went to Launchpad with .Skype_Upgrade still there, clicked on it which resulted in a question mark over it, then I attempted to drag it to the Trash and it vanished.
I think re-installed Skype and everything now seems fine and dandy.
I don't know if this will help you but I figured I'd post my experience here in hope that it does help.
Thanks
Brendan.