My daughter's Bullie, Chloe has dry eye. She uses baby wipes to clean the gunk out...same method you use. Moving the gunk from the middle of Chloe's eyes to the corner. My Bullie, Punkie doesn't have dry eye but she does wake up with eye gunk each morning but her's is mostly on the outer edges of her eyes and is easily cleaned off with a baby wipe. What you say about your Shih-Tzu is funny because my daughter and I both have what we call "nurse" dogs. My daughter has a male chihuahua and he makes sure all her dogs have clean faces and ears! My little "nurse" dog, Zoei is a rescued terrier mix...she keeps my all her pack mates ears and faces cleaned up. My Bullie, Punkie has a deep tail pocket and Zoei tries to clean it but I have to finish the job when she starts it because she leaves Punkie's tail pocket wet...so after she cleans it, I dry it throughly and put some powder on it. Gotta love DOGS!