I don't know myself. I did some looking and found the following. According to this it wouldn't harm your yorkie. You can read it. I will post the item and the link where I found it.
12/27/2007: Hilary from San Tan, Arizona writes: "100% Natural Oregano oil in capsules ; 2 capsules twice a day for a week or so, about 2 to 5 drops of oregano oil per capsule with a carrier agent like grape seed oil (about 12 drops). You can get the essential oil at most nature type food stores and the empty capsules. Within a few days you will notice a huge difference in your dog and within a week no more coughing and back to normal. You can also sterilize your home of germs and viruses by putting about 15 to 20 drops in a humidifier and running it. Your house will smell like a wonderful italian kitchen and the house will be sanitized!"
Home Remedies to Cure Coughs, including Kennel Cough, in Dogs.