How to keep Ajax refresh action when 'Use Ajax' option is disabled? I have disabled 'Use Ajax' because I don't want AJAX pagination. Unfortunately other Ajax functionality stopped working.

How to ajaxify View programmatically?
@sumit madan's approach then is the best, leave your view ajaxified, and remove the paging, simplest seems to me by overwriting this method of the behavoir in your theme:

/**
 * Attach the ajax behavior to each link.
 */
Drupal.views.ajaxView.prototype.attachPagerAjax = function() {
  this.$view.find('ul.pager &gt; li &gt; a, th.views-field a, .attachment .views-summary a')
  .each(jQuery.proxy(this.attachPagerLinkAjax, this));
};


just make it an empty function (add this code in your theme behavoir)

Drupal.views.ajaxView.prototype.attachPagerAjax = function() {};


this function also needs to be overwirtten:

Drupal.views.ajaxView.prototype.attachPagerLinkAjax = function() {};