Custom permalink question

What you need is to register your own Rewrite Rule. To do it you should use add_rewrite_rule function.

function my_custom_external_rewrite_rule() {
    add_rewrite_rule('^post-type-name/([^/]+)/?', 'index.php?page_id=<PAGE_ID>&external_page_name=$matches[1]', 'top');
}
add_action( 'init', 'my_custom_external_rewrite_rule' );

And you’ll have to register your custom query variable (using query_vars hook):

function my_custom_external_query_var( $query_vars ) {
    $query_vars[] = 'external_page_name';
    return $query_vars;
}
add_filter( 'query_vars', 'my_custom_external_query_var' );

This way requests to post-type-name/slug/ will cause displaying page with and you will be able to obtain the slug of external post with get_query_var( 'external_page_name' );