This is not possible with current functionality but you can go ahead with modification from your end and we will assist you. You will have to look into the GetWtiLikePost function present in wti_like_post_site.php file.
We are not sure why you say that you have to refresh the page to show the updated like/unlike count also why you have created a shortcode for that. May be there is some javascript conflict with your theme after the like/unlike activity is processed. Please share your site url.
Thanks