If its XP see:
Using TweakUI to change the shortcut arrow icon is more safer. Plus, it offers another special icon Light Arrow (icon within TweakUI.exe). This gives the user an extra option to set the shortcut arrows to Light Arrow style, without completely removing the arrow.
Not sure if that works with Vista.
For vista Checkout; http://www.winhelponline.com/articles/153/1/How-to-remove-or-modify-the-Shortcut-overlay-in-Windows-Vista.html