I haven't taken any excursions in Panama or Belize; only Costa Rica.
You should always buy travel insurance in case the unthinkable happens. The cruise lines and the tour operators put your safety first; but accidents do happen. There have been at least two fatalities this year due apparently to negligence: a cave tubing accident and a zip line accident. But there have also been fatalities at Disneyland; so there is an element of risk in everything.
I have only been to Puntarenas on the Pacific side and I imagine you are going to Limon if you are doing the partial Canal transit. From what I've heard Limon is not a place to be wondering around on your own. But I would not hesitate to try the rafting or zip line on a ship-sponsored excursion. But if you are concerned about safety, remember, Costa Rica is an absolutely beautiful country. Just a bus tour into San Jose is a wonderful experience.