@Gy273,
I think it "sounds" fine, as far as everyday speech goes.
That said, it probably is a double negative, if you consider it to be all one statement. This might be more apparent if you re-arrange the word order as follows:
"I don't think this (is/isn't) paper."
But, I would look at it as more or less a new sentence. This would be clear, for example:
This isn't paper. At least I don't think it is.
You are simply adding the proviso that you don't claim to be certain, that way.