Hooking into add_submenu_page

Hook into admin_head, the last action before the menu is rendered, and change the global $menu:

add_action( 'admin_head', 'wpse_71303_change_menu_cap' );

/**
 * Change the capability to access an admin menu item.
 *
 * @wp-hook admin_head
 * @return void
 */
function wpse_71303_change_menu_cap()
{
    global $menu;

    foreach ( $menu as $key => $item )
    {
        // Find menu by name
        if ( 'Tools' === $item[0] ) // default cap: 'edit_posts'
        {
            $menu[ $key ][1] = 'new_capability';
        }
    }
}