Private Page – Error 404

Is there ANY way to make a page visible, but NOT part of the navigational menu?

Yup, how you do it depends on how your menu is built

look for your menu code, probably in header.php

if you use wp_list_pages, we can exclude certain pages

If you use wp_nav_menu you can build a menu using the appearance->menu menu, and just put what you want in the menu

there are plugins, but it’s easy to use wp_list_pages to exclude pages from your menu, but still have them exist and be able to be visited

http://codex.wordpress.org/Function_Reference/wp_list_pages#Exclude_Pages_from_List

This plugin may help too, Ive never used it tho
http://wordpress.org/extend/plugins/exclude-pages/