I used plarn (plastic bag yarn) instead of fabric, and an old broken trousers hanger (one of the pegs was broken and I broke the other one off with pliers) instead of the wire hanger (I need those for other projects :P)
I didn't have sturdier cardboard so I joined the rings so that they overlap. I was worried the plarn could be too slippery to hold the scarves in place, but it's not - now I'm only worried if the print from the plastic bags will rub off on them...