I've got a couple of comments to make:
1. In an ideal world, you're preventing an event from happening. I'm not sure how well a Concealed Carry permit is going to help unless you have enough warning to pull the weapon, warn off the potential attacker, they have time to realize "this is stupid" and then turn around and run.
2. This is more than just a gender issue. I'm sure it's true for most photographers that once the camera comes up, our situational awareness changes. We are not seeing things the same way we would if there was no camera. I had a tripod develop "legs" when I was shooting at Great Falls with a couple of spectators who walked by, I turned around and it was gone. There are a number of instances where photographers have made the news b/c they were a victim of a robbery or crime....camera gear is attractive and relatively easy to fence.
3. Anything you can do to deter a possible incident is better than having to respond to an attack. I say this b/c...quite simply, if you're responding, the chances are that you're caught by surprise and your chances of handling your weapon (be it a taser, pepper spray, a gun, whatever) aren't good. Even trained professionals (military and cops) will get caught unprepared and fire wildly or not at all--that's part of the principle behind the "Model Mugging" program (that you can carry a weapon or learn martial arts and when you get surprised you fail to use it). If you think I'm exaggerating on this, I want you to think of how many times you were out hiking with your camera at the ready and you missed that elk who jumped across the path or the eagle taking off from the branch over your head or the bear that ambled across the creek crossing. Great shots and you were fumbling to get your camera out or lens cap off and never got off a shot (or it was horribly out of focus). And that's with something (your camera) that you've probably used more often then you any weapon you're likely carrying. I agree with Lew on this point about the likelihood of guns being effective for situations like this. But even if you disagree and decide to get a permit to carry and you train, do realize there is a significant chance that if you're jumped, you'll never get your gun out.
4. So from my perspective, the best options are a combination of planning and situational awareness:
--Think through where you're going to shoot. If it's new territory for you, find people who've shot there before that can give you a better feel for the area. Sometimes you may decide to take a pass on an area b/c you don't have a good feel for the safety level.
--Always carry a cellphone and check to be sure you've got coverage in that area. If not, reconsider if you want to go there. Separate from an attack or crime, you can always break an ankle or a decaying floor gives way and you fall through and find yourself in an unbeaten area unable to get yourself out.
--Pay attention when you get in to parking lots. See if there are police or park rangers near by. Get a sense of who's likely to be in that area and what resources are available (other hikers, police) you can call on. Pick up a map of the area (that shows paths, cabins, rest stops, phone kiosks, etc.
--Consider a companion. Another shooter or two. Join a photo meet-up group and then coordinate shoots to places at the time you want to shoot there. For instance, I set up a night-time shoot on the DC Mall to shoot the Lincoln Memorial, the US Institute of Peace, etc....we got lots of females shooters...but we had safety in numbers (and a couple of them told me this). A dog can be a good asset (even if he's not big or an "attack" dog). BTW, here's a hint if you own a dog...teach him to bark or growl on command. And your command for your dog to growl is: "no bite, no bite." Tell that to a dog that is growling and most approaching individuals will figure they can't "friend" their way past the dog, they're going to take a couple of bites (even from a small dog) and like reconsider.
--As you shoot, always take quick breaks to put the camera down and look round you. Check the environment. Listen for other hikers. Scan for anyone who's being a voyeur of sorts. I had a chance to talk to a Brit who had gone through the British Jungle Warfare School in Malaysia...where they do their jungle training. He was taught that when you're out in the boonies you stop every couple of minutes and just take the lay of things...see if you hear any unordinary sounds, a flock of birds suddenly taking flight, and that when you do this as a habit...you start to acquire a sense that warns you "something's different."