Check out the Benchmade Griptilian range, particularly the Mini in yellow. The plain edge would be good for camping, although a slightly longer blade would be better. The size and color might help with your folks' reluctance. Lots of good suggestions for knives. Single blades are lighter, but people will think them are more weapon like since there aren't other tools in there to dilute the view.
As for your parents, don't give up hope that they will come around. Sounds like they are working off what they see in the media, without the benefit of positive personal experience. Over time you yourself can provide that positive influence by demonstrating both your own maturity and responsibility and that such a tool can be useful in ways they haven't thought of. A lot of people who haven't got used to knives as tools have had to find alternative ways to do things and can be surprised that a knife can be as handy as they are. At the end of the day, you want to go outdoors and do things where your safety and comfort will be enhanced by having a knife as a tool. That can be made as a sensible and well reasoned argument.
When I was a bit younger than you I wanted to get into shooting air rifles and hunting small game. I was lucky in that I had been allowed to carry a knife since I was six, but my mum had always been totally anti guns, to the point she didn't want to buy water pistols or cap guns when I was little. It took a while, but I did get her permission, and my folks even drove me to the other side of our (small) country to buy my first rifle. I had to talk through all the emotional reasons she didn't like guns, try to see things from her side and then present counter arguments that addressed her fears. It took some patience, which in itself is a good thing to demonstrate

, and some time.
Technical details always make things sound boring. You want your choice of knife to sound like it is boring and you want it for a long string of technical reasons that have nothing to do with style, drama, cool, or prestige value with your friends.
I am sure you will be able to persuade your parents if you can keep them talking long enough

I wish you the very best of luck!!!
Chris