I'd say shoot for Elkmont you should have no problem at all I was there today and they have opened up another area there were plenty of sites.
As far as the gun no need leave it at home.
I would bring the waders you can fish longer and more comfortable with them.
No sense in wasting a day away hiking there is plenty of great water to fish right through the campground.
There is some nice water that can be reached easy just up Little River Trail. enjoy your trip.