Do install TweakUi.
You now can no longer say "everybody".
Actually the way TweakUi removes the shortcut arrow is better than how other tweak utilities do it.
TweakUi replaces the shortcut arrow icon overlay with a transparent one, the other modify the registry value for LNKFILE.
The latter way often causes duplicate items in Explorer context menus.
It is possible to do it without TweakUi,
change or create this registry key
HKEY_LOCAL_MACHINE\ SOFTWARE\ Microsoft\ Windows\ CurrentVersion\ Explorer\ Shell Icons
29 REG_SZ C:\Windows\System32\shell32.dll,51
reboot
You may have to delete the icon cache (iconcache.db in C:\Documents and Settings\your username\Local Settings\Application Data)
and kill and restart the explore.exe process in task manager.
TweakUi is easier.