As of 2010 carry is legal in NP's as long as you have a valid permit in that state. SMNP is in TN and NC. Make sure your permit is good in both states, or stay only in the state where you're legal
Carry is legal in the woods, not inside a building owned by the Fed's though. Make sure before you go inside.
SMNP is probably the most populated area for black bear in the USA. You likely will see bear at that time of year. A lady was killed by a bear there in 2000 and a small child just outside the park in 2006 I think it was. There have been several incidents in recent years where hiker/bear incidents have happened. A hiker was bitten on the foot and the bear killed 2-3 years ago.
I think a $30-$40 can of bear spray is a better defense. Of your choices I'd take a .40 loaded with heavy bullets. I hike there often and carry my G-20. Seen lots of bear, never felt threatened. But I do believe in being prepared.