There is a trick I learned where you can hide the menu in a Pane.  When creating or editing your skin, wrap the menu in a pane (that you will not use), and add the following attribute to the pane:

<div id="HideMenuPane" runat="server" visible="false">[SOLPARTMENU]</div>

What this does is hide the menu to everyone that is not logged in.  However, this may not be the optimal solution for you, as it only hides the menu from visitors without user accounts.  Once they log in, it will be visible. 

Another workaround would be to create a module that incorporates the menu in it, show it on all pages, but only to the Admin role.

Hi

What sort of module.  A custom one?

Cheers