I think exponential discounting already assumes uncertainty. You need uncertainty to discount at all - if things are going to stay the same, might as well wait until later. And it doesn't intuitively lead to hyperbolic discounts - if there's a 1% chance you'll die each week, then waiting from now until next week should make you discount the same amount as waiting from ten weeks from now until eleven.

But there is a way to use uncertainty to get from exponential to hyperbolic discounting. You get exponential if you're worried about yourself dying/being unable to use the reward/etc. But if you add in the chance of the reward going away, based on a prior where you don't know anything about how likely that is, you might get hyperbolic discounting. If you don't eat an animal you've killed in the next ten minutes, then it might get stolen by hyenas. But common-sensibly, if it goes a year without being stolen by hyenas or going bad or anything, there's not much chance of hyenas suddenly coming along in the next ten minutes after that.