Copterhead - it sounds like you need to look at the Canadian military SAR technicians' job - they are free-fall, mountaineer, diver, rescue swimmer, survival expert, winchman and all-round tough guy rolled into one.
The sheer size and variation in geography of their SAR area means they are often dropped in from FW to the casualty in order to stabilise them whilst the helicopter takes 2 or 3 days to transit to recover them.
In UK, the RN stopped having divers aboard SAR helicopters a few years ago - partly due to the training burden and partly because a diver is only useful in a very small minority of SAR situations whereas a winchman is what you want for the vast majority of them.
The only UK SAR job I have heard of with someone being swept into a cave in the last 15 years was in Devon and that person was rescued by a winchman.