I wrap one layer of cotton over another, then add seven coats of shellac. There's a very slight give to the doubling of the wrap, yet it remains thin enough that it doesn't look bulky to my eye. As much as I love and prefer the look of cotton vs. "cork," I fall into that camp of people who love the feel of the wrap even more. Double win in my opinion.
Here's an example - two layers of cloth...only a touch thicker than a single layer and seems to fit my palms and grip nicely.