Resolvi o problema adicionando IN BOOLEAN MODE à seção contra a instrução conforme abaixo:
SELECT `prod_id`
FROM (`product_search`)
WHERE MATCH (`prod_title`, `prod_desc`) AGAINST ('silk' IN BOOLEAN MODE)
OR `prod_id` LIKE '%silk%' OR `prod_sku` LIKE '%silk%'
OR `prod_title` LIKE '%silk%'
OR `prod_desc` LIKE '%silk%';
