Here's the way I would do it, using CandyBar to replace the icons. Just create a blank icon, or something with only a few pixels and is completely transparent. Then, use Candybar to change the alias icon for the system. Should work fine.
I'm sure there's a way to do it via a Mitthrawnuruodo-type administrator-level trick to change the finder and trashcan icons as well, but Candybar makes it easy.
Edit: or just do it the way iMeowbot suggests 🙂