Alternatively, all the resort shops and park shops sell 'sleeves' for the bands in different designs in cotton. Maybe that would solve the problem? Or perhaps you have a fine jersey 'sweat band' you can put on your wrist and wear the band over that?
I found my wrist got a bit sweaty under the band: I could have got round ths by wearing it a bit looser, of course.
It's just that it's so convenient to have the band instead of a card to keep fishing out of your bag or pocket, and I hate things round my neck like lanyards and stuff.