The laws are a funny thing WC. NJ is full of vagueness where weapons are concerned.
Consider your statement that you can keep a loaded weapon in your house legally in NJ. If you have children, not so. It can be loaded, but it must be locked in a secure manner and inaccessable to any children. And if you want to use it, guess what? NJ is NOT a "Castle State" so if someone attacks you in your home, legally you have to run out the back door or jump through a window if possible before attempting to defend yourself or your family. Assisted opening knives (NOT autos, ASSISTED OPENING) are sold in NJ, but illegal to possess. Carrying a fixed blade in public is illegal.
So the best advice I can give a fellow NewJerseyite Under communist oppression that is forced, or chooses of their own volition to "bug out" is:
It is all about "intent". Leaving with loaded weapons, or unloaded weapons in NJ for the purpose of defending yourself is an illegal act.
Listen closely....YOU ARE NOT ALLOWED TO DEFEND YOURSELF IN NEW JERSEY WITH A WEAPON....PERIOD. You are not allowed to possess ANY weapon for defense. The closest you can get is 3/4 oz of pepper spray. All firearms and knives are illegal to carry for defense. Stun guns are illegal, PR-24's and night sticks are illegal. Slingshots are illegal. BB guns require a firearms ID card.
If you have a reasonable fixed blade knife in your camping gear for use in camp, your "intent" was a legal one and you should be fine.
Technically speaking, you would have to commit the crime of illegal weapons transport to make it to the border of another state which has more common sense, then you are legal with the aformentioned firearms.