Remove Skype From the Taskbar Using This Option
Windows: If you are using Skype, you may know that getting Skype out of the taskbar is unusually difficult. If you want the application to remain active without taking up all of your space, select this option.
As the Into Windows tips blog points out, there is a button in Skype advanced settings that will allow you to remove Skype from the taskbar when you’re signed in. To access it, go to Tools> Options> Advanced Settings and uncheck the Save box. Skype on the taskbar when I’m signed in. “
How To Remove Skype Icon From Windows 10 Taskbar Without Exiting | On Windows