hmm this is a lot of hassle for such a small thing! but anyway...
the desktop icons are stored in c:\documents and settings\all users\desktop
if you open that and see all the icons, copy them all, and then go to each users desktop bit (c:\documents and settings\*user name*\desktop) and paste them into there.
so if you have 3 users on one computer you will need to paste all the icons into each users folder! and then delete them all from the shared directory.
so now you should be able to delete ones from your own desktop without deleteing things from everyones!
hope this works,