Mmmmm.... NOPE! National Park... Felony... BIG trouble... But by now, you know this.
Actually, this is a problem in my part of the world. There are LOTS of national parks, and it's rather difficult to keep up with where the boundaries are. As part of my martial arts class, we go over some jo (short staff) techniques specifically for use with your "walking stick" on the trails. (My "walking stick" is a jo with a furniture stopper on one end!)
I trust you're either going to Gatlinburg or Pigeon Forge? Both are in a dry county, which means that you can be pretty safe carrying into the eateries on the strip. And, you can leave the pistol in the car while you're on the hiking trails.
The Smoky Mountain hiking trails are pretty safe. There are people EVERYWHERE, so you don't have to worry much about personal security. The only real thing to worry about is the bears, but honestly, if you find a bear and don't have the common sense to leave it ALONE, then you DESERVE whatever happens to you! (Every year we hear about some tourist who gets eaten by a momma bear after they try to go "pet" the bear cubs. The feds always go kill the bear, but they never address the fact that the tourist basically had it coming.)
So, recap: Gun in car? Check. Gun on the strip? Probably check. Gun on trails? Negative. Bears? Cute, but not for petting.