Exclude categories from custom blog archive page

Ok I am working on a site that has an existing custom Archive page that was done by a freelancer. It’s a bit too complicated for me to make the edit that I need to make.

Basically the client is using certain categories for different content that they don’t want to show up on the blog Archive page.

So I think I need to edit the query to the database to exclude the certain categories:

if ( ! empty( $category__in ) ) {
		$join = " INNER JOIN $wpdb->term_relationships ON ($wpdb->posts.ID = $wpdb->term_relationships.object_id) INNER JOIN $wpdb->term_taxonomy ON ($wpdb->term_relationships.term_taxonomy_id = $wpdb->term_taxonomy.term_taxonomy_id) ";
		$where .= " AND $wpdb->term_taxonomy.taxonomy = 'category' ";
		$include_cats = "'" . implode("', '", $category__in) . "'";
		$where .= " AND $wpdb->term_taxonomy.term_id IN ($include_cats) ";
	} else {
		$join = apply_filters('getarchives_join', "", $r);
	}

Any help would be much appreciated!

Here is the complete function in functions.php :

function custom_archives($args = null) {
	global $wpdb, $wp_locale;

	$defaults = array(
		'type' => 'monthly', 'limit' => '', 'category__in' => array(),
		'format' => 'html', 'before' => '',
		'after' => '', 'show_post_count' => false, 'show_posts' => true
	);

	$r = wp_parse_args( $args, $defaults );
	extract( $r, EXTR_SKIP );

	if ( '' == $type )
		$type = 'monthly';

	if ( '' != $limit ) {
		$limit = (int) $limit;
		$limit = ' LIMIT '.$limit;
	}

	// this is what will separate dates on weekly archive links
	$archive_week_separator = '–';

	// over-ride general date format ? 0 = no: use the date format set in Options, 1 = yes: over-ride
	$archive_date_format_over_ride = 0;

	// options for daily archive (only if you over-ride the general date format)
	$archive_day_date_format = 'Y/m/d';

	// options for weekly archive (only if you over-ride the general date format)
	$archive_week_start_date_format = 'Y/m/d';
	$archive_week_end_date_format	= 'Y/m/d';

	if ( !$archive_date_format_over_ride ) {
		$archive_day_date_format = get_option('date_format');
		$archive_week_start_date_format = get_option('date_format');
		$archive_week_end_date_format = get_option('date_format');
	}

	$add_hours = intval(get_option('gmt_offset'));
	$add_minutes = intval(60 * (get_option('gmt_offset') - $add_hours));

	//filters
	$where = apply_filters('getarchives_where', "WHERE post_type = 'post' AND post_status = 'publish'", $r );
	if ( ! empty( $category__in ) ) {
		$join = " INNER JOIN $wpdb->term_relationships ON ($wpdb->posts.ID = $wpdb->term_relationships.object_id) INNER JOIN $wpdb->term_taxonomy ON ($wpdb->term_relationships.term_taxonomy_id = $wpdb->term_taxonomy.term_taxonomy_id) ";
		$where .= " AND $wpdb->term_taxonomy.taxonomy = 'category' ";
		$include_cats = "'" . implode("', '", $category__in) . "'";
		$where .= " AND $wpdb->term_taxonomy.term_id IN ($include_cats) ";
	} else {
		$join = apply_filters('getarchives_join', "", $r);
	}

	if ( 'monthly' == $type ) {
		$arcresults = $wpdb->get_results("SELECT DISTINCT YEAR(post_date) AS <code>year</code>, MONTH(post_date) AS <code>month</code>, count(ID) as posts FROM $wpdb->posts $join $where GROUP BY YEAR(post_date), MONTH(post_date) ORDER BY post_date DESC" . $limit);
		if ( $arcresults ) {
			$afterafter = $after;
			foreach ( $arcresults as $arcresult ) {
				$url	= get_month_link($arcresult->year,	$arcresult->month);
				$text = sprintf(__('%1$s %2$d'), $wp_locale->get_month($arcresult->month), $arcresult->year);
				/* Query posts for that month */
				$after = '';
				if ( $show_posts ) :
					query_posts(array('monthnum' => $arcresult->month, 'year' => $arcresult->year));
					while (have_posts()) : the_post();
						$after .= '<div class="post">
						<h3><a href="' . get_permalink() . '" rel="bookmark" title="Continue reading ' . get_the_title() . '">' . get_the_title() . '</a></h3>

						<div class="blog-post">

							<h4>' . get_the_time('l, F jS, Y') . ' at ' . get_the_time('g:i A') . ' EST ' . '<a href="' . get_edit_post_link( $post->ID ) . '" title="' . __( 'Edit post' ) . '">' . $link . '</a>' . '</h4>

							' . get_the_excerpt("Continue reading...") . '

						</div>
					</div>';
					endwhile;
				endif;
				if ( $show_post_count )
					$text = $text . '&nbsp;('.$arcresult->posts.')';
				if ( $show_posts )
					echo get_archives_link($url, $text, 'html', '<h2>', '</h2>' . $after);
				else
					echo get_archives_link($url, $text, 'html', '', '' . $after);
			}
		}
	}
}