Keep in mind with all my advice here, I am not a parent by any stretch. I don't think I even have the patience to deal with young children, so i applaud you. But my dad did teach me some survival skills as a kid (he truly is a wog at heart) so I can see what affect his advice had on me.
I say that even though children should be protected from the bad things in the world, they should learn to protect themselves. you can't protect them forever. They should also know why, children should understand that even though most people are good, there are some bad people in the world.
I say don't focus on the violence until they are older, you have to make sure they understand violence is generally bad and should be avoided if possible. Martial arts are good for this. Your 11 year old there might be old enough to grasp the concept of when not to and when to use violence.
Instead focus mostly on the good. teach them if something bad happens, that what you teach them will help them protect themselves and at the same time help people who are not as lucky.
Start steering away from the gear, make sure they are not dependant on it. Go camping, don't use a GPS or compass (keep them on hand to be safe) teach the kids to navigate by the sun and the stars, how to improvise shelter. Because they are so young you can even make a game of it. You said your kids are in scouts, so they should already be getting some of this knowledge. And you geocache, so they obviously know how to use GPS to navigate.
As for violence, I say martial arts is probably one of the best options. It is generally regarded as good to have your kids in some form of martial art. But be careful not to put your kids in too many activities at once. Also if you are into it, you could start taking them hunting when they get into their teenage years. This is a practical skill, teaches firearm discipline, and you get a couple months of good meat out of it too (if you know what you are doing). Of course, hunting isn't for everyone, you could even go to a firing range occasionally (when they are older) to teach them how to handle a real weapon, and paintball to teach the tactics of it. Paintball is popular, easy to get into, and i have seen kids as young as 5 get into it and in some cases even be a better shot than myself! With hunting and shooting range, some people really frown on that, paintball has the added advantage of 'it's just a game!' Which gets rid of alot of the social stigma about it.
Keep in mind, none of my advise is given from a parents perspective, so all should be taken with a grain of salt. I have no idea what it's like to be in your position, so just use your WOG-sense (better than common sense because wogs arent common