I’m going to answer my own question:
SELECT ID FROM wpyw_posts
WHERE ID NOT IN (
SELECT wpyw_term_relationships.object_id
FROM wpyw_term_relationships
INNER JOIN wpyw_term_taxonomy ON wpyw_term_taxonomy.term_id = wpyw_term_relationships.term_taxonomy_id
WHERE wpyw_term_taxonomy.taxonomy = 'product_tag'
) AND wpyw_posts.post_type="product"