This problem is finally fixed with Skype 18.104.22.168 for Linux. This makes the question obsolete for every one who installed Skype directly from the website. Version 4.0+ will be included in the universe repositories for Quantal (Ubuntu 12.10).
Just a little unnecessary annoyance to fix here:
Suppose you have Skype for Ubuntu running. You accidentally click on the launcher again. The way it is now, Skype starts a second instance, which promptly tells you it can't log in. There is another instance already running. To make things worse: On the next regular start of Skype it you will have to re-enter your saved password, due to the "Sign in failure".
I thought this would be fixed soon but neither Canonical nor Microsoft care enough. The annoyance continues to exist for the last three updates at least. So in an approach to provide a workaround I will post what I've done to prevent this behaviour. Maybe it's useful for some of you. Maybe it will rise awareness and cause a fix.
I'm happy for any better solution btw. and that's the real purpose of my question. Usually I don't answer them myself. So doesn anyone know of a better solution to fix dual instancing of Skype?