I'm pretty sure the jam is made from the fruit, the tunas. I could be wrong. I think I've seen the paddles sugared as candy, but again, I don't pay much attention to it as it is not a favorite. I will now though
I'll keep my eyes out for it.
Personally, I wouldn't try the paddles unless they came already peeled and without thorns. Doing it without getting hurt is a talent you might have to learn young, the trial and error part could be painful. Every store here has a lady behind a kiosk peeling the nopales and you can get them whole or cut in strips. It's a lot easier.