Adding a query string to only one page url

You can filter page_link to modify the output of any page’s permalink value. The simplest way to identify the page is by ID, then you can append the query string via add_query_arg:

function wpd_append_query_string( $url, $id ) {
    if( 42 == $id ) {
        $url = add_query_arg( 'ngg_force_update', 1, $url );
    }
    return $url;
}
add_filter( 'page_link', 'wpd_append_query_string', 10, 2 );