I'm not sure on the exact thread count but what you can do is wet the pillow case you are trying to use. If you can still easily breath through it when its wet there should be no problems for the snake when it is dry or if it happens to urinate in the bag. This is what I did when I was soaking trying to get a stuck shed off and had similar concerns.

The thread fibers expand when wet and this is when you really need to worry about suffocation.