Rope is easy to restring with. Plus it's a lot tougher than you think. Just get standard rope, even nylon rope I would think would work.
Set up the chucks like the pick. And burn away. My first fire chucks where with cord and I had absolutely zero problems. If you hold them so the fire climbs up the chuck then yeah, the tubing will get hot. But you don't do that. Your spinning like a mad man and having a blast. And if you aren't spinning your holding them up like a torch.
Never had any issues using plain old chord. It never caught on fire, (the flames where over 10 inches away) and I never had string break on me. Mainly cause I did quick checks every now and then. To have a rope break on you in mid spin seems kind of irresponsible on the chuckers part. I know accidents happen. But it seems silly.
Nylon chord might cause issues IF you hold the chucks so the flame crawls up melting the chord slightly and then cooling makeing it crisp and more breakable. Other wise, same thing goes.
Just check the strings (by checking the strings I mean, the .3 second look and quick yank) and all should be good.

When you yank on the wire hard with string( REALLY HARD) it bends the wire up, and keeps the chord from sliding back and forth. I never noticed any skipping while spinning with chords like this.
btw - bailing wire is tuff, it's going to last a long time. I've never swapped out my bailing wire ever since I started chucking.
Oh and the tubing I used wasnt thin sharp stuff. I just grabbed some aluminum tubbing from a hardware store 1" diameter with a 1/8" thick wall. Then it wont ding on you bad or bend.