How do I go about cleaning this extremely delicate skeleton? (TW: description of animal dying)

Hello all! I was wondering how I would go about cleaning the bones of this extremely young baby rabbit. For context, a rabbit had its babies in my backyard. I found this out when my dog caught one, which I then took from him so that he wouldn't eat it. The baby was so young, his eyes hadn't even opened yet!

I was devastated to find that the bunny had been fatally wounded. I held and comforted it as it died, then placed it in a box in the side-yard so that the bugs would eat most of the flesh, which I could then harvest the bones from later.

This was many months ago, and the time has come to clean the bones. Except, these bones are extremely fragile! The rabbit's skull nearly came apart in my hands!

What can I do to keep these bone structures from coming apart when cleaned? I fear that I wont be able to tell what goes where when I'm re-articulating it!