How to add (css) classes to only one wp_nav_menu()?

I’m going to start by saying something similar to Horttcore..

Is there a reason you can’t simply provide a differing container element for the given menu, it should provide enough specificity to style it uniquely.

Although, you could do something like this to conditionalise menu args based on the menu’s location..

function my_wp_nav_menu_args( $args="" ) {
    if( $args['theme_location'] == 'your-specific-location' )
        $args = array_merge( array(
            'container_class' => 'example',
            'menu_class' => 'example2'
        ), $args );
    return $args;
}
add_filter( 'wp_nav_menu_args', 'my_wp_nav_menu_args' );

Above code is based on the example given on the codex page for wp_nav_menu, and could easily be extended to do any number of things.
http://codex.wordpress.org/Function_Reference/wp_nav_menu

Hope that helps..