You can change this registry key to show a new arrow overlay (in your case, a blank one):
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\Shell Icons\29 (may or may not have /29 on the 32 bit version)
Just change the key to say point to the file, followed by ",0"
e.g. :
C:\Windows\Shortcut.ico,0
Here's a blank ico file you can use (attached as zip)