Is it possible to give the user the chance to select between two single template files to use in a post?

If the differences in the pages are just query arguments the you can add query vars and use them in the same template:

//add your arguments to query vars
add_filter('query_vars', 'my_query_vars');

function my_query_vars($vars) {
    // add my_sortand ptype to the valid list of variables you can add as many as you want
    $new_vars = array('my_sort','ptype');
    $vars = $new_vars + $vars;
    return $vars;
}

your query should look like this:

<?php $custom_posts = new WP_Query(); ?>
<?php $custom_posts->query(array('post_type' => get_query_var('ptype'), 'order' => get_query_var('my_sort'))); ?>
<?php while ($custom_posts->have_posts()) : $custom_posts->the_post(); ?>
    <div class="content-block-2">
        <a href="https://wordpress.stackexchange.com/questions/13086/<?php the_permalink(); ?>" title="<?php printf( esc_attr__( 'Permalink to %s', 'twentyten' ), the_title_attribute( 'echo=0' ) ); ?>" rel="bookmark"><?php the_title(); ?></a>
    </div>
<?php endwhile; ?>

and you links for the user should be:

• ASC: url + ?ptype=bbp_topic&my_sort=ASC
• DESC: url + ?ptype=bbp_topic&my_sort=DESC

Now if your differences in the pages are more then query arguments you can change the template page using template_redirect hook:

same as before add your query arg

   //add your arguments to query vars
    add_filter('query_vars', 'my_query_vars');

    function my_query_vars($vars) {
        // add my_sort to the valid list of variables 
        $new_vars = array('my_sort');
        $vars = $new_vars + $vars;
        return $vars;
    }

then add a function to the template_redirect hook and create the redirection based of that argument:

add_action("template_redirect", 'sort_template_redirect');
// Template selection
function sort_template_redirect()
{
    global $wp;
    global $wp_query;
    if (isset($wp->query_vars["my_sort"]))
    {
        // Let's look for the template file in the current theme
        if (array_key_exists('my_sort', $wp->query_vars) && $wp->query_vars['my_sort'] == 'ASC'){
            include(TEMPLATEPATH . '/single-asc.php');
            die();
        }
        if (array_key_exists('my_sort', $wp->query_vars) && $wp->query_vars['my_sort'] == 'DESC'){
            include(TEMPLATEPATH . '/single-desc.php:');
            die();
        }
    }
}

and once again you will need to add the args to the link so:

• ASC: url + ?my_sort=ASC
• DESC: url + ?my_sort=DESC