We went to Hato Caves last week on our Equinox trip. It was very hot in the caves, so I would recommend grabbing a bottle of water before leaving the ship and dressing comfortably. I was surprised we weren’t required to wear closed toe shoes but at the very least I would wear sandals with a strap and not flip flops.
We had a fabulous time on the Equinox doing the same itinerary as you will be doing. Also, sailed in a balcony cabin after only sailing in the Retreat on E class ships post Covid. Murano was a treat with amazing food and service. Tuscan for the elite breakfast was a nice quiet alternative to the buffet, someplace we never went when we had access to Luminae.