Hello, No, a dog cannot get rabies from licking a small wound. It can only be caught from a bite.
I am sorry, I have been doing some more research, and it appears that they may be able to get rabies if the wound has the rabies virus. Here is an article about a dog licking a human wound and why it could cause rabies:
Rabies is transmitted through contact with the saliva of an infected animal. Bites are the most common mode of Rabies transmission but the virus can be transmitted when saliva enters any open wound or mucus membrane (such as the mouth, nose, or eye). As a result, licks or scratches from rabid animals can also transmit the virus.
Canines, particularly dogs, are the most common source of Rabies transmission worldwide because they bite readily and often have contact with humans and other animals. Canine Rabies – a specific type of Rabies that is spread among dogs, foxes, coyotes, wolves, and other canines – is still endemic (meaning it is regularly found) in parts of Africa, Asia, and Central and South America. In these regions, there are significant challenges to reducing Rabies in canines such as low vaccination rates in dogs, limited and costly veterinary services, lack of public awareness, and uncontrolled dog populations.
Most Rabies deaths occur in Africa and Asia and are due to bites, scratches, or licks from dogs. In Europe, Canada, and the United States, human Rabies cases are rare because most dogs are vaccinated against it. In these regions, Rabies is most often reported in wild animals such as raccoons, skunks, and foxes.