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If they're the icons with the arrow, they don't have anything to do with the app except pointing to it. They're a file in their own right: "Firefox.lnk". So if you delete them, you won't do anything to the app.
You can check this by looking at the properties of the shortcut, and you have the safety that delete only puts it in the recycle bin, until you empty it, it's trivial to put the shortcut back.
You cannot remove the shortcut sign from applications, because as rsmith said, they are default on .lnk
you may try this.... http://www.howtogeek.com/howto/windows-vista/disable-shortcut-icon-arrow-overlay-in-windows-vista/