|Hi Angie, that would work but I think it would be awfully harsh on the dog's coat because alcohol is so drying and they do not have as much natural oils on the hair. Plus, we have to think about the residue and what may be absorbed by the animal's skin and tongue when they lick themselves.
I think a better solution would be to put on some gloves and a raincoat if you have one to protect yourself from the oils, and give your pet a bath with shampoo made for humans. It contains stronger detergents than dog shampoo because our hair gets oilier faster than an animals. First, make sure your dog's fur is well saturated with warm water, then shampoo, let sit on the coat for a minute, rinse, shampoo again, and rinse. I am sure all traces of oil will be gone but the fur will not be damaged. Make sure you pay special attention to the foot pads, tummy area, and ears because they often get missed. Place cotton in the ears before the bath to keep water out because their ears are susceptable to infection when water gets in the canals. Dry your dog with an old towel or paper towels. Don't let it outside until it is dry, or they may go roll in something right away~ LOL! You can always use a blow dryer on them also if you want.
If your dog has a bed, special pillow, etc. that they sleep on, you will need to wash that too, before the bath, or the dog will recontaminate itself and you. Wash alone in hot water with a good detergent like Tide. I think it is best to let items with urushiol oil on them soak for at least 30 minutes in the wash cycle, just to make sure the oil is all dissolved, and then turn your machine back on and continue washing. Hope you get better soon.