プレビュー画面内に公開ボタンを設置

自己解決致しましたので、共有しておきます。

以下のコードで出来ました。

single.php

<?php if(current_user_can('read_private_pages')) : ?>
<?php
$url = add_query_arg(array('action'=>'mypublish', 'post'=>$post->ID),home_url());
echo  "<a href='" . wp_nonce_url($url, 'my-publish-post_' . $post->ID) . "'>公開する</a>";
?><?php endif; ?>

function.php

if(isset($_REQUEST['action']) && $_REQUEST['action']=='mypublish')
    add_action('init','my_publish_draft');

    function my_publish_draft(){
         //Get the post's ID.
         $post_id = (isset($_REQUEST['post']) ?  (int) $_REQUEST['post'] : 0);

        //No post? Oh well..
        if(empty($post_id))
            return;

        $nonce = $_REQUEST['_wpnonce'];

        //Check nonce
        if (! wp_verify_nonce($nonce,'my-publish-post_'.$post_id))
            wp_die('Are you sure?'); 

        //Check user permissions
        if (!current_user_can('publish_posts'))
            wp_die("You can't do that"); 

        //Any other checks you may wish to perform..

        //Publish post
        wp_publish_post( $post_id );

        //Redirect to published post
        $redirect = get_permalink($post_id);
        wp_redirect($redirect);
        exit;
    }