Elastic in towel wraps

I’m looking to purchase a good 100% cotton or linen towel wrap for the sauna (cover from chest to knees). I’m not comfortable with nudity (please do not try to convince me otherwise) so am looking for a wrap that would give me a bit more reliable coverage than a towel. However, almost all of them have elastic at the top. Is this an issue? I heard that the polyester and elastic in bathing suits can be an issue (along with chlorine) but then I’ve seen many wraps with elastic sold and recommended.

The only option I can find without elastic is Uwrapt and they look thinner than I’d like.