It really does seem to be the object that people are afraid of and not the one who wields it.
I just got into my office from the NY Knife show. One of the people there asked me what I got, when I showed her the knife in the sheath and then pulled the knife out of the sheath gentily, with 2 fingers, she backed away startled (knee jerk reaction). A few other people in the office however looked at it with interest and even asked to handle it.
I think in part it has to do with exposure, use, need and especially familiarity.
Most people in cities don't have guns, never grew up with them in their homes and have an irrational fear of them. Exceptions seem to be with families with spouses that were/are in the military or law enforcement. People in rural areas however seem more accepting of firearms.
I do get nervous around a few power tools, like the radial arm saw because I know what it can do; but I still use it carefully.
The same I would say applies to knives. My father always had a knife, an electricians knife. He went to High School for electronics and trained in the Navy durng WWII. For him it was an everyday tool. My mother is a good home cook and used quite a few knives. I have had a knife since I was about 9, we did a lot of camping so there was always a knife or hatchet around. I started learning how to cook around age 12 to 15.
I've been cut alot with knives, and a few razor blades, had a few stitches, but I've never been afraid of them.
