You would say it when you probably will do the activity you are discussing. It implies that you cannot think of something really awful that might happen. I don't that it matches the idea in the first sentence.
I assume that you mean
I don't want to go skydiving, or perhaps
I wouldn't want to go skydiving.
Maxiogee Jnr did a parachute jump for charity last year. He thoroughly enjoyed it. Prior to the jump the trainer wanted to get the group thinking more seriously, as they were getting a bit 'giddy' at the prospect of the jump, and asked them "What's the worst that can happen to you?"
One of them offered "We could be killed?"
"No," said the trainer, "you might live if you're really unlucky."
The immediate impact of the unmentioned prospect of a bed-bound or wheelchair-bound paraplegic settled them down promptly.
We are lacking context. We don't know what the person is trying to say.
Theoretically, he could be expressing hesitation; the question could be asked in an attempt to prompt a reassuring reply.
I don't think I want to go skydiving...Well, ok,...tell me, what's the worst than can happen to you?
I'm thinking of situations when you internally do kind of what to do something, but are slightly apprehensive. You would ask such a question to get the other person to sort of "spell it out" and make it absolutely clear that things will be ok.
I know it's a stretch - the above scenario is quite unlikely - but the point is that we're really in the dark when we don't have context.