Rather than ask a bunch of questions, I'm going to answer this from a general sense about the pros and cons.
Which park are you going to?
-NC Law allows open carry in a motor vehicle, and allows open carry in areas outside of public-owned buildings, on the grounds or parking areas of those buildings, and public parks and recreation areas where further regulations MAY restrict those rights.
How populous is the area you're going to be?
-If you're concerned about how other people are going to react, then it really matters how many people you're likely to interact with (for multiple reasons). If you're through hiking and don't expect to see many people, you are ALSO more likely to encounter wildlife. If you're doing a day hike out and back and will likely run across 20+ other groups then you're almost guaranteed not to run into any sort of predatory wildlife.
Since you're worried about cultural implications and perception, this will play into it a lot more in people's minds as well. If the farthest you're going is 2 hours away from the car park, you're more likely to be perceived as carrying it 'just because' in my opinion. If you're on a multi-day hike and in an area that's known to have more frequent bear activity (I say more frequent because bear encounters in western NC are still pretty rare), you're more likely to get a pass. Even the most anti-gun people I know are a little more understanding in situations like that, but understand that many people will forego stopping for a bit to chat with someone who is openly carrying.
Lastly, consider a flare gun, if this really bothers you. There are better ways to scare off a bear than with a gun. Both for you AND the bear. I can't conceive of a single scenario where a gun is going to keep you from getting bit from a snake, but a flare gun might get you found. A flare gun is more likely to be useful if you break your leg than a regular gun. For most other animals, a flare gun is going to be sufficient to drive them off if you do find yourself in the astronomically low odds of an actual attack.