If you have a Skype shortcut on your desktop, you can't change the icon. You have to create a new shortcut by right clicking on the desktop then >new >shortcut. The file path is "C:\Program Files\Skype\Phone\Skype.exe" or "C:\Program Files (x86)\Skype\Phone\Skype.exe" for x64 systems. After creating the shortcut, you right click it then click Properties and there is a Change icon button or something like that, i'm not sure, because i'm not using Windows in english. In the next windows you click browse and select the .ico file on your computer. This icon I uploaded is a .png file, on Windows, you have to use this: [link]
On Linux, you can simply use the .png image.