Western Union is one of the safest ways to transfer funds, perhaps second only to bank wire transfers. I have sent money by Western Union a number of times, and never had any problem.
Once the money is in WU's hands, and you have been notified by WU of the fund transfer, you should feel safe to ship the product.
Once the money is in WU's hands, and you have been notified by WU of the fund transfer, you should feel safe to ship the product.