I really don't think there's any disease that you're bound to pick up from these dead little souls. I carry hand wipes in my car as I'm often stinking of sardines etc. in my haste to get a trap set for kittens etc. I encounter. I do the same if I see a dead cat on the road, as even the animal control many times won't bother. I usually have a bag of some sort in my car to pick them up in. In a pinch I can usually find a box in a dumpster if not. I'm two minutes away from the vets who will bury them for me free of charge. It's the least we can do for those who don't make it. Thank you from me and the cats you pick up.