While some shampoos are designed to be used for different pets, we advise that you be cautious before using your cat shampoo on your whippet. It would be best if you have a dedicated shampoo for your whippet to be able to cater to its sensitive nature. However, if you are going to use your cat's shampoo, ensure that it is hypoallergenic, and does not contain irritants or other ingredients that can harm your puppy.