That looks like a human tattoo needle type machine. You HAVE to anesthetize a dog to use one of those---think of how bad tattoos can hurt on people. Try that with a dog and you can see how they will potentially freak out. I'd like to see how they do it.
The National Dog Registry Tattoo Does Not Hurt Your Pet
Pet tattoos are not like human tattoos, because there are distinct dimensional differences between the structures of human and animal skin. The epidermis, or top layer of skin, on a human is much thicker, and the lower skin layers are more uneven than the layers of canine or feline skin. The epidermis is the layer of skin that dries up and flakes off, so to tattoo effectively, the ink must be inserted just below it. On humans, the tattoo must go much deeper into the skin, because of the thickness and uneven shape of the epidermis. Canine and feline epidermis is much thinner and is very regular and even. As a result, the tattoo does not need to penetrate as deeply into the skin.
The epidermis has only tactile sense, the sense of touch that allows you to feel surface contact. There are no "pain sensors " in the upper layers of skin. Because the tattoo needle does not reach the nerve endings of a cat or dog's skin, it is highly unlikely your pet will experience serious discomfort. The only sensation your pet will feel is the vibration of the marker.
Most pets, especially dogs, are easy to tattoo. However, animals generally dislike being held still on their sides, and some also dislike the sounds the clippers and some older tattoo markers make. Some pets' tactile senses are more pronounced than others, and they react when the vibrating marker touches their skin. Remember, your pet is in unusual surroundings, around strangers, and may be nervous. These factors alone sometimes are enough to make your pet voice his or her displeasure. If you stay calm, your pet will stay calm too.
A good amount of tummy tickling helps during the process. Never scold or yell at your pet--use a calm, reassuring tone to let him or her know that you are there and that everything is OK. It is up to you! The safety provided by a registered tattoo far outweighs any momentary nervousness you or your pet might experience. At tattoo demonstrations, we often ask volunteers to touch the tattoo marker tip while it is running (without ink, of course). They are always surprised that it simply does not hurt.