The challenge sounds so cool. I was hoping to hear that you use the cords for dance too, haha.
I would if I needed them - rsk8d's experience with the rocker indicates that I might do so again in the future. I used to use them for camel spins mostly. So far in dance it hasn't been an issue, I think because I've done enough ballet.
There really isn't a wrong way to use them, once you know how to fasten them onto your skate (they come with a diagram - it's pretty easy) Standard way is to use 2 cords, connecting each hand to the corresponding foot, although, as has been said, there are tons of ways to use them. All they do is make you more aware of your body position and extension because as you stretch the cords you can feel better where everything is. You don't do special exercises in them, you just work as you normally would, but your awareness is heightened.
My kids are using them now for stroking, to feel the extension of the free leg and to hold their arms up instead of flopping around like wet noodles - also to increase their awareness of core. (I have a couple of noodle-y skaters!) We do a couple laps of stroking, then forward and backward crossovers in a figure-8 pattern, 3 times around for each, then we work on their spiral positions. I've also started having them do a few waltz jumps before I let them take the cords off, because I want them to hold their landing positions with nice extension. They whine about how "hard" it is, but both are using the cords for a good 10 minutes in their lessons. We'll see how well they do on their own when the challenge starts this weekend!
The biggest concern with these, or any similar training aid, is that the elastic would break under tension and snap back at the skater, so if you make your own, be sure that any connections are very secure.