Yes, Turpentine is safe for all animals that I know of. It's the liquid blood of the pine tree. I remember hearing a story of a hunter in eastern KY and his dog got bitten by a copperhead or rattlesnake to the face. Poor dog head was swollen to the size of a basketball. Some people told him to put the dog down. But, he decided to rub turpentine with a cottonball all over the dog's head. He repeated this several times during the day. The swelling came down and the dog lived into his old years.
If the dog has a large mass, I would also give them turmeric powder in their food. Adjust dosage to weight.
Turpentine and Kerosene are universal healers.
My grandmother was my babysitter til I was 10 years old. Anytime one of us kids got a cut, sting or scrap, she would put kerosene on a nasty rag and wipe the area. It was the only medicine I knew of til I got older. lol