(I'll get pictures up in a bit)
Okay, one of my graphite sticks' cord seemed to be growing weak, so it's time to restring! I use a method that allows the nunchaku to be detached. To string this way, you must do each stick individually.
This is how I do it... your mileage may vary.
What I use is two... small poky things. One is the end of a compass (the geometrical kind, not the geographical kind) and another is some sort of stick. The compass end is quite a bit thinner and more maneuverable.
And, of course, you need some cord. I use nylon/polyester cord, and in my experience it's very strong (I had to cut my weak graphite cord off because I spun them for a couple hours and they wouldn't break!) One of the problems with this method is that you don't exactly know how long of a cord you need until you get to the end of it... I just tried and got it too short. Luckily, cord isn't that expensive and restringing this way isn't all too difficult if you have to retry. Cut a generous length, since it's possible to cut off excess at the end to get the right final cord length you like. Basically, you can have too little cord but not too much. It seems that you'll need about 14" to be comfortable (considering that I just barely failed using 12")
If you're using graphites and have never restrung before, then you'll need to get set up. You may as well do your first restringing when the manufacturer's cord snaps. After that, you'll have to break some sort of hard brownish resin-like adhesive material off. They originally added this stuff to glue the cord into place... I guess because they can't be bothered to string the things properly. For our purposes, glue isn't needed. To break this stuff off, I used the compass end, since it's great at picking/scraping. After that, you'll have to slide the manufacturer's cord out, which is rather easy once the glue is off.
Now, take the cord you cut and fold it in half. Slide the two cut ends down the hole in the head of the nunchaku. Now, here's the hardest part of the method. Take one of your stick object and try to push both cord ends over to one side by pushing the stick through the opposite side. This may take a bit of fiddling. Try to keep the cords running straight through this whole tutorial, rather than crossing over each other. It's easier if you broke all that glue stuff off. Try a blunt stick first. If you can't do it, try a sharp end. If you still can't do it, use a smaller sharp stick (in my case, the compass), poke into the cord, and drag it out. Fiddling with this may damage the cord, which is generally okay, but try not to do it too much or you may have to retry.
Once the cord ends are all the way through that hole, push them through the lower hole on that side, back to the original side. Use the same method. It should be easier this time, since the cords will already be facing horizontally. When you're done with that, pull them up and push them back into the last hole, which is the hole you originally pushed the stick into. If the cord is getting too tight, use some method to drag more cord down from the other side. I poke the compass into the cord and drag it down. Then pull it on the other side to where you need more.
Now, you'll have to try to get the cords all the way through the original vertical hole. Try poking them diagonally through the previous hole. Once they're through, tie a knot with the two cord ends. It might not need to be a particularly strong knot. The idea is simply to enlarge and entangle the cords such that the cord can't go back down the vertical shaft.
Now you should have a single nunchaku stick with a loop at the top. The loop should be big enough to fit around the other stick of your nunchaku. If it's not, then you used too little cord and need to redo it. The final cord length will be about double of the length of the loop, assuming you do both sticks with about the same length cord.
When you're done, pull as hard as you can on the loop to test the security of it. It's better to find out now that you mechanism is insecure than to have a stick fly off during a real trial (I know from experience...)
