The problem is solved - thanks to all who responded!
Especially the tip from @PeterJones and @Coises has brought me closer to the solution, I now knew where to look.
It was actually registry entries (from “Open Command Prompt here” Context Menu), which I have been using since Windows 7 (without the problem). And since it was so handy, of course I used that on all my systems.
That’s where Win10 behaves differently than Win7.
Source: Enhancing the “Open Command Prompt here” Context Menu experience
After removing these registry entries the problem is solved.