You might find it easier to sweep up with a soft brush. I pick them up out of the run with my fingers, no gloves, but I don't find bunny poop to be gross really, maybe I'm a bit gross though :lol:
They should get the hang of litter training if you put the poops where you want them to do them. Buns like to munch whilst they poop and wee so putting hay in or near to the litter tray helps.
I don't think poop is too much of a hazard in terms of flies as it should be very dry and crumbly but their first poops (their caecotrophs which they should eat straight away) are sticky and smelly so if they have excess caecos I would make sure you clear them up and look at their diet as they shouldn't be leaving those.
Hope this helps.