One of the the biggest dangers of handling dead wild birds is the risk of catching an arbovirus (ie arthropod-borne virus), from one of the many mites,ticks and parasites that live on these animals at any given moment. It's no joke, I was infected by one of these lovely little bugs in the middle of Pretoria suburbs and was hospitalized for 10 days. Fun side- effects I was experiencing was bleeding from the eyes, encephalitis, meningitis(which earns you a Lumbar puncture) and pretty much every "-itis" as all my body's organs were under attack. Lost 10kg muscle weight during my stay. Took painful weeks to recover strength again. Not one of my fondest memories. I think freezing kills most insects.
The main bacterial risk comes from the blood.
Bottomline: Be careful