Denying via 404 instead of 403

I have the following setup for phpmyadmin:

<Directory /usr/share/phpmyadmin>
        Options FollowSymLinks
        DirectoryIndex index.php
        Order Deny,Allow
        Allow from 127.0.0.1
        Deny from all

...

</Directory>

So essentially, I only allow phpmyadmin to be accessible from localhost. If someone from the outside world attempts to go to http://mydomain/phpmyadmin they'll get a 403 (Forbidden). This might tip them off to the fact it's there, but they just can't get to it.

Question: I'd rather have Apache return a 404 in this instance. Is that possible?