I agree with Frank. If you do decide to hike alone, make sure someone knows the trail you are taking, time you are heading out and take a GPS because cell service can be splotchy. Also make sure you have emergency gear: emergency blanket, whistle, flashlight, first aid kit, food and plenty of water for you and your dog. Keep eyes and ears open for hogs, goats and mountain lions as well as snakes. Make sure you are off the trails before sunset because it gets dark in the canyons before it does in higher elevations. Just a side note: personally, I would not hike alone because of the high risk of injury due to terrain. Because of loose rock and type of vegetation. I just wouldn't risk it.
I think it unlikely that you would be unsafe from other humans. That said, there are places where a slip and fall could easily occur, and I have seen a wild hog and signs of others. Your small dog might look like an attractive snack to a predator. If at all possible, I recommend you bring a friend to hike with.
I hiked alone when I last went. Dog would be fine on a leash only SP rules
Thanks! Your answer is awaiting moderation.