What you're actually looking to do is to implement a custom Views Display Extender plugin (https://api.drupal.org/api/views/views.api.php/group/views_plugins/7.x-3.x).

It's not particularly trivial and I got most of my information from this wonderful tutorial here: [How to write a Views Plugin Display Extender (D7) by Bryan Ollendyke][1]

Here's a basic outline:

-create a custom module (let's call it mymodule) and implement [hook_views_api()][2].

    /**
     * Implements hook_views_api().
     */
    function mymodule_views_api() {
      return array(
        'api' => 3,
        'path' => drupal_get_path('module', 'mymodule'),
      );
    }

-Create a mymodule.views.inc file (remembering to add the file to your mymodule.info file) and implement [hook_views_plugins()][3]. It should look something like this:

    /**
    * Implements hook_views_plugins().
     */
    function mymodule_views_plugins() {
      $path = drupal_get_path('module', 'my_module');
      $plugins = array();
      
      $plugins['display_extender'] = array(
        'mymodule' => array(
          'title' => t('Some Setting'),
          'help' => t('A description of the setting.'),
          'path' => $path,
          'handler' => 'mymodule_views_plugin_display_extender',
        ),
      );
      
      return $plugins;
    }

-Note the "handler" index in the above array. You'll need to implement that in a file called mymodule_views_plugin_display_extender.inc (again, remembering to add that in your mymodule.info file). The implementation should look something like this:

    class mymodule_views_plugin_display_extender extends views_plugin_display_extender {
      /**
       * Provide a form to edit options for this plugin.
       */
      function options_definition_alter(&$options) {
        $options['my_setting'] = array(
          'default' => 0,
        );
      }
    
      /**
       * Provide a form to edit options for this plugin.
       */
      function options_form(&$form, &$form_state) {
        if ($form['#section'] == 'page-mymodule') {
          $form['my_setting'] = array(
            '#type' => 'checkbox',
            '#title' => t('Some Setting'),
            '#description' => t('A sample checkbox.'),
            '#default_value' => $this->display->get_option('my_setting'),
          );
        }
      }
      
      /**
       * Handle any special handling on the validate form.
       */
      function options_submit(&$form, &$form_state) {
        $this->display->set_option('my_setting', $form_state['values']['my_setting']);
      }
    
      /**
       * Provide the default summary for options in the views UI.
       *
       * This output is returned as an array.
       */
      function options_summary(&$categories, &$options) {
        $options['mymodule'] = array(
          'category' => 'other',
          'title' => t('Some Setting'),
          'value' => ($this->display->get_option('my_setting')) ? 'Yes' : 'No',
          'desc' => t('Set a setting.'),
        );
      }
      
    }

After all that your mymodule.info file should look something like this:

    name = My Module
    description = Sample views display extender
    core = 7.x
    version = 7.x-1.0
    
    dependencies[] = views
    
    files[] = mymodule.views.inc
    files[] = mymodule_views_plugin_display_extender.inc

If that all works out, you should see a setting show up under "Other" (you can change that using the 'category' in the options_summary implementation in mymodule_views_plugin_display_extender.inc.

After that, in your module, you can access the option from the view using something like:

    $view->display_handler->get_option('my_setting');

For instance, if you were implementing `[hook_views_post_execute()][4].

    /**
     * Implements hook_views_post_execute().
     */
    function mymodule_views_post_execute(&$view) {
      $my_setting = $view->display_handler->get_option('my_setting');
    }



  [1]: https://drupal.psu.edu/blog/post/how-write-views-plugin-display-extender-d7
  [2]: https://api.drupal.org/api/views/views.api.php/function/hook_views_api/7.x-3.x
  [3]: https://api.drupal.org/api/views/views.api.php/function/hook_views_plugins/7.x-3.x
  [4]: https://api.drupal.org/api/views/views.api.php/function/hook_views_post_execute/7.x-3.x