Oh, no.
This will force them to rely almost entirely on the limited animals on the map. If I were the opponent, I would definitely kill all the animals as fast as I can to limit your food and coin income.
On the other hand, mines will become exclusive resources for other civilizations because you don’t have any means to use mines. When you have to start using estates since you run out of animals, your opponent still has many natural mines to get coins, which will be a huge disadvantage.
Why not create a “hunting hut” and make it relate to tribal marketplaces similar to the relation between shrines and cherry orchards?