Adding an extra parameter [string] to my posts’ permalink?

The Codex page for post_link has an example similar to what you need. For custom post types, there’s also the post_type_link filter.

This would go in your theme’s functions.php, and checks if a meta key query_arg exists, and appends it to the URL if so:

function wpa_post_link( $url, $post ){
    if ( $meta = get_post_meta( $post->ID, 'query_arg', true ) ) {
        $url = add_query_arg( 'param', $meta, $url );
    }
    return $url;
}
add_filter( 'post_link', 'wpa_post_link', 10, 2 );