Best I'm aware, MySQL doesn't have much of a regexp replace functionality -- not to mention its very clunky regexp syntax. So this is easiest to do at the php level. Start by fetching all posts that have the shortcode:
$posts = $wpdb->get_results("
SELECT ID, post_content
FROM $wpdb->posts
WHERE post_content LIKE '%[zdvideo]%'
");
And then loop through the result:
foreach ($posts as $post) {
$post->post_content = preg_replace(
"/\\[zdvideo\\](.+?)\\[\\/zdvideo\\]/",
"$1", # $1 holds the url... format as needed
$post->post_content);
# Be sure to verify on a few posts before actually saving...
# var_dump($post->post_content);
$wpdb->query("
UPDATE $wdpb->posts
SET post_content = " . $wpdb->escape($post->post_content) . "
WHERE ID = " . intval($post->ID)
);
}