Removing the Shortcut Arrows on Desktop Icons

Go to Start > Run
type:  REGEDIT.EXE

Backup the Registry using, File > Export for each of the following Keys.

 
Open the Directory:  HKEY_CLASSES_ROOT

then

Open the Key:  lnkfile
Rename the value IsShortcut to IsNotShortcut

Open the Key:  piffile
Rename the value IsShortcut to IsNotShortcut

Open the Key:  InternetShortcut
Rename the value IsShortcut to IsNotShortcut

Reboot

To revert back to default, either rename each value to IsShortcut, or
simply double click each of the backups for the Keys that were saved.
Answer "Yes" when asked if you'd like to merge the values.