Display all product tags associated with a specific product category

Ahh ha! Have figured out how to do this. Here’s the code for future people who are looking for the same thing:

function get_category_tags($args) {
    global $wpdb;
    $tags = $wpdb->get_results("
        SELECT DISTINCT terms2.term_id as tag_id, terms2.name as tag_name, terms2.slug as tag_slug, null as tag_link
        FROM
            wp_posts as p1
            LEFT JOIN wp_term_relationships as r1 ON p1.ID = r1.object_ID
            LEFT JOIN wp_term_taxonomy as t1 ON r1.term_taxonomy_id = t1.term_taxonomy_id
            LEFT JOIN wp_terms as terms1 ON t1.term_id = terms1.term_id,

            wp_posts as p2
            LEFT JOIN wp_term_relationships as r2 ON p2.ID = r2.object_ID
            LEFT JOIN wp_term_taxonomy as t2 ON r2.term_taxonomy_id = t2.term_taxonomy_id
            LEFT JOIN wp_terms as terms2 ON t2.term_id = terms2.term_id
        WHERE
            t1.taxonomy = 'product_cat' AND p1.post_status="publish" AND terms1.term_id IN (".$args['categories'].") AND 
            t2.taxonomy = 'product_tag' AND p2.post_status="publish"
            AND p1.ID = p2.ID
        ORDER by tag_name
    ");

    $count = 0;

    foreach ($tags as $tag) {
        $tags[$count]->tag_link = get_tag_link($tag->tag_id);
        $count++;
    }
    return $tags;
}

$args = array('categories'=> "YOUR PRODUCT CATEGORY ID HERE"); 
$tags = get_category_tags($args); 

foreach ($tags as $tag) {   
    echo '<a href="'.$tag->tag_link.'">' . $tag->tag_name . '</a>';  
}

I used this in a WP Bakery shortcode and it worked a treat. I guess you could use this wherever you would like. Enjoy!