Here is how to remove the pesky taskbar icon of skype on Windows 10 and move it into the tray:

Right click on the skype shortcut entry or the skype executable in your Explorer, select settings (or properties) and then open the compability tab.
There set the option to start in Vista SP2 compability and apply.

Restart Skype completely (if you don’t know how to do it, then restart your whole computer)

Skype should now only be visible in the systemtray when minimized.