My best advice is to be VERY careful. The Rangers don't care much for any type of animal / landscape disturbance - and any offense in a National Forest can turn into a Federal Offense. Your safest bet is just to hope you come upon something.
The Smokys are right down the road from me, and I steer clear of flipping while I am hiking.
However, if you are prone to do some flipping anyway, you will find more salamanders than just about any other place in the world. And the Hellbenders, if you can find them, are quite impressive.
As far as snakes go, I have seen more Black Rats, Black Racers, and Garters than anything else. There are Black Kings as well. I, personally, have never seen a Copperhead nor Timber Rattler, but again - I don't flip.
Smoky Mountain National Park is a beautiful place to visit. Watch the gnats and mosquitoes, and you should have a great trip!