Ditto on the limestone, when wet only spikes will do. Tread is the key. Nothing big and clumsy, you might catch an edge and... The local Guatemala folks wore nothing but slick sandals, and seemed very confident.
On asending and desending, zig-zag back and forth. Like five steps one way and five the other. This keeps your shoulders at a angle to face and is much more comfortable and less scary.
Tikal for three days was rough on this couch potato:) I'd do it again and again...