Get cookie value via ajax?

Question

Drupal

Hello. I'm stupid.
The situation is as follows, there is a created view (view), which displays the nodes. This view has the ability to sort, I store the value for sorting in cookies, which I take in hook_views_query_alter and, based on this value, I use one or another sort for the view.

function hook_views_query_alter(&$view, &$query) {
  if($view->name == 'product'){

    # Сортировка полей
    $sorting_field = 'default';
    if(isset($_COOKIE['sorting_field'])){
      $sorting_field = $_COOKIE['sorting_field'];
    }

    $sort_default = $view->query->orderby[0];
    $sort_price_asc = $view->query->orderby[1];
    $sort_price_desc = $view->query->orderby[2];

    unset($view->query->orderby[0]);
    unset($view->query->orderby[1]);
    unset($view->query->orderby[2]);

    # Дефолтная сортировка (по дате)
    if($sorting_field == 'default'){
      $view->query->orderby[0] = $sort_default;
    }

    # Сортировка по цене (по возрастанию)
    if($sorting_field == 'price_asc'){
      $view->query->orderby[1] = $sort_price_asc;
    }

    # Сортировка по цене (по убыванию)
    if($sorting_field == 'price_desc'){
      $view->query->orderby[1] = $sort_price_desc;
    }

  }
}

at this stage everything is fine. Also, of course, there is a custom form from the module, which contains sorting options

function hook_form($form, &$form_state){

  $form = array();

  # Ctools autosubmit
  ctools_add_js('auto-submit');
  $form['#attributes']['class'][] = 'ctools-auto-submit-full-form';

  # Сортировка
  $sorting_options = array(
    'price_asc' => 'цена 1',
    'price_desc' => 'цена 2',
    'default' => 'без сортировки'
  );

  $form['sorting'] = array(
    '#type' => 'select',
    '#title' => 'Сортировать по:',
    '#options' => $sorting_options,
    '#default_value' => isset($_COOKIE['sorting_field']) ? $_COOKIE['sorting_field'] : 'default',
  );

  $form['submit'] = array(
    '#type' => 'submit',
    '#value' => 'Сортировать',
    '#ajax' => array(
      'callback' => 'skate_product_sort_form_submit',
      'event' => 'click',
    ),
    '#attributes' => array('class' => array('ctools-use-ajax', 'ctools-auto-submit-click')),
  );

  return $form;

}

and accordingly submit

function hook_form_submit($form, &$form_state){

  # Время хранения cookie
  # По умолчанию на 30 дней
  $time_cookie = time()+60*60*24*30;

  # Домен
  $domain = str_replace('http://', '', $GLOBALS['base_root']);

  # Сохраняем в куки сортировку по полю
  $sort_field = $form_state['values']['sorting'];
  setcookie('sorting_field', $sort_field, $time_cookie, '/', $domain);

  $commands = array();

  # Результат представления
  $result_output = views_embed_view('product', 'page');
  $commands[] = ajax_command_invoke('.selector', 'html', array($result_output));

  return array('#type' => 'ajax', '#commands' => $commands);

}

Now the question is how to make this work through AJAX, because the new value in the cookie will be available only after the page is refreshed. Or is it possible to also update the HTTP headers via AJAX before calling hook_views_query_alter ? Maybe the gurus solved this?