Well, I'm not sure where to look in the registry, but the way I'd do it until I found a better way would be this:
Get rid of the icon from your desktop by right-clicking on desktop, properties, desktop, customize desktop, and un-tick internet explorer, then just create a shortcut on your desktop, targeted to "C:\Program Files\Internet Explorer\iexplore.exe", and starting in %HOMEDRIVE%%HOMEPATH%, then just select the icon you'd like to use.