Dynamically link to the latest post or simulate request of specific post in page template

I want to have a link in the wordpress menu pointing to the latest post of a specific category.

Because I am not able put a dynamic URL in the wordpress menu, my approach was to put a page with a custom page template in the menu.

This page template should behave like the themes single.php but showing that last post from the given category.

Is there a way to include the themes single.php and simulate a request of a specific post?

I tried to copy the content of single.php in a page template and modify the query with

query_posts( array( 'cat' => 9993, 'showposts' => 1) );

If I do that before the_header(), then I will get no posts. If I do it after the_header(), then I get the correct content but the header of the theme will set some specific classes for styling a page. So I need the the_header() function to think the desired post was requested and not the page.

Update:
I did not completely use the solution by toscho because I did not get the active menu entry highlighted and in the right position with that. But he pointed me in the right direction with the wp_nav_menu_objects filter.

I had a main-menu item CategoryX which should open directly the latest post from CategoryX, and also opening a sub-menu with links to older posts and other related things. The sub-menu should have also a link to the latest Post (LatestFromX) in it, which should also be highlighted directly after klicking on CategoryX in the main menu.

What I basically did was: Creating dummy menu items with the WP admin backend and then replacing its URL with the filter function.

function wp_menu_add_last_from_category_x( $sorted_menu_items, $args ) {   
    global $wp;

    // get url of latest article in CategoryX (CategoryX has id 9993):
    $latest = get_posts( array( 'numberposts' => 1, 'category' => 9993 ) ); 
    $latest_url = get_permalink($latest[0]->ID);

    // search for the dummy menu items and replace the url:
    foreach ($sorted_menu_items as $key => $item) {
        if ($item->title === 'CategoryX' || $item->title === 'LatestFromX') {
            $sorted_menu_items[$key]->url = $latest_url;
            if ($wp->request == $latest[0]->post_name) {
                $sorted_menu_items[$key]->classes[] = "current-menu-item";
            }
        }
    }

    return $sorted_menu_items;
}

You can filter wp_nav_menu_objects and add a new item. Here is a simple plugin doing that:

<?php # -*- coding: utf-8 -*-
/**
 * Plugin Name: Latest Post In Menu
 * Description: Append a link to the latest post to all nav menus called with the argument <code>'add_latest_post' => TRUE</code>.
 * Plugin URI:  http://wordpress.stackexchange.com/q/59892/73
 * Version:     2012.07
 * Author:      Thomas Scholz
 * Author URI:  http://toscho.de
 * License:     MIT
 * License URI: http://www.opensource.org/licenses/mit-license.php
 */

add_filter( 'wp_nav_menu_objects', 'wpse_59892_latest_post_in_nav_menu', 10, 2 );

/**
 * Add a link to the latest post to the nav menu.
 *
 * The nav menu has to be called with 'add_latest_post' => TRUE.
 * Example:
 * wp_nav_menu(
 *  array(
 *      'theme_location' => 'primary',
 *      'add_latest_post' => TRUE
 *  )
 * );
 *
 * @wp-hook wp_nav_menu_objects
 * @param   array $sorted_menu_items Existing menu items
 * @param   object $args Nav menu arguments as object.
 * @return  array
 */
function wpse_59892_latest_post_in_nav_menu( $sorted_menu_items, $args )
{
    if ( ! isset ( $args->add_latest_post )                    // argument set?
        or ! $args->add_latest_post                           // argument TRUE?
        or ! $latest = get_posts( array ( 'numberposts' => 1 ) ) // post found?
    )
    {
        return $sorted_menu_items;
    }

    // Uncomment the following line to see what you can change:
    // print '<pre>' . htmlspecialchars( var_export( $sorted_menu_items, TRUE ) ) . '</pre>';

    $post    = $latest[0];
    $content = empty ( $post->post_excerpt ) ? $post->post_content : $post->post_excerpt;
    $link    = array (
        'title'            => $post->post_title,
        'menu_item_parent' => 0,
        'ID'               => '',
        'db_id'            => '',
        'url'              => get_permalink( $post->ID ),
        'classes'          => array (
                0 => '',
                1 => 'menu-item',
                2 => 'menu-item-type-post_type',
                3 => 'menu-item-object-post',
                4 => 'latest-post',
            ),
        // strips all tags and reduces the length to 20 words
        'attr_title'       => wp_trim_words( $content, 20 ),
    );

    $sorted_menu_items[] = (object) $link;

    return $sorted_menu_items;
}

If we write a new post …

… and call the nav menu like this …

wp_nav_menu( 
    array( 
        'theme_location'  => 'primary', 
        'add_latest_post' => TRUE 
    ) 
);

… we get …

The nav menu item has a class latest-post, so we can style it per CSS:

.menu .latest-post a
{
    color: #eee;
    background: #9f0;
}