I found the solution myself. As I said I use a 4k Monitor but I've set the Windows 10 scaling to 175%. In order for the Skins to look right one then has to set the "High DPI-Settings" on the Compatibility Page in the properties dialog window for the Application. There you have to check "Overwrite High-DPI-Scaling" and set it to "System". If you set it to "System Extended" you get the effect I showed in my first Screenshot. Excuse me, if the translations for the Settings are wrong, but I have a german system.
Here is a Screenshot:
And a picture showing the TheaterMode:
Thank you very much for thinking about the problem.