Since it appears you want all access to IE to occur through your special link, you will always want to suppress the display of the special IE system icon on the desktop, perhaps replacing it with a standard shortcut to your program. As Kent says, you can suppress the icon display by GPO. If you'd rather not use Group Policies (though I certainly recommend them if possible!), you can also turn off the icon display directly by a registry entry--see Hide the Internet Explorer Icon. Doing it through a registry entry rather than by GPO, the setting may not take effect until the user logs off and back on (that is, removing the IE icon that way, it may still show for the first session). It's the equivalent of going into Internet Options, Advanced, and (un)checking "Show Internet Explorer on the desktop," so if you're not doing it by GPO, be sure you've restricted students' ability to turn this back on in Internet Options.

Joe