First, declare the after arg at the beginning of your code:
$args['before'] = '<div id="link_wrap">';
$args['after'] = '</div>';
When there is a next page, the arg is overwritten, so you’ll have to add the closing tag at the end:
if ($page<$numpages) # there is a next page
$args['after'] = ' '. _wp_link_page($page+1)
. $args['link_before'] . $args['nextpagelink'] . '</a></div>'
;