"Open air" caving compared to cave diving is blissfully safe.
Absolutely. Cave diving is like being an underground astronaut. You air supply can really crimp your chances of survival.
Dry caving, as long as you don't fall or get trapped head-down and die, you can live for days. If you had the common sense to leave an itinerary the rescue crews can go down and get you. Most cavers carry water and a little food. Staying calm, not doing anything stupid and waiting for the cavalry to arrive is often the best emergency plan.
Thousands of people dry cave and very few get seriously hurt, fewer still die. I have run a few trips into caves as a guide for people who have never done it before and nobody got seriously hurt. A twisted ankle, a bunch of sore, overworked and banged up knees (Florida caves have long stretches where you have to crawl), and maybe a dozen minor scrapes. Everything was taken care of on-site with basic first-aid supplies. In my opinion everyone should try a trip into caves just so they know what they are about.
Of course being rescued isn't always easy. They might, if there is a difficult squeeze between your location and the exit and you're unable to maneuver under your own power, they break your collar bones so your more streamlined. More rarely, in caves with a lot of very tight turns, they might also break the long bones in the leg. People kind of slither through when the bones are not in the way.