Now that we have migrated from Skype for Business to Teams, it is no longer necessary for the Skype application to start when you log on to your computer.

Click on the Skype for Business icon in your task bar.  When the Skype application shows on the screen, click on the Gear icon.

Click on Personal on the left menu

Remove the email address.  Uncheck the option to Automatically start the application when I log on to Windows

Click OK to close that screen.

Click on the Arrow next to the Gear.

Select File, Exit to close the program.

The Skype icon will likely continue to show in your taskbar but will not start automatically.