Well, I have no idea what Scunci's No Damage ponytail elastics are made of, probably nylon or something. They're basically a nylon stocking type tube cut into sections, each section rolling up a bit and becoming a ponytail elastic. Maybe you can't find a petroleum free ponytail, but I was just thinking you might be able to buy some bamboo or cotton stockings and try and make your own like Scunci's. They would probably be bigger and looser, and you'd have to loop it around more times, but it might work.
ETA: Another idea. You can find natural office rubber bands, and cover them. If you crochet, you can cover them with crochet stitches. Or you could sew a cover for them. I used to crochet covers for regular ponytails, I'm sure you could do the same with a rubber band.
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