Actually in my headcannon the blood vessels and nerves atatch on theyr own and grow if needed so that transplants would be MUCH easier!
The fluffy body is well engineered and FASCINATING!
Though “it was a toy” is good logic to start a canon idea.
Some early Fluffy works portrayed them as modular, able to reattach limbs by contact. They were also immune to infection.
All you have to do is reverse-justify it with wacky mad science.
So say Fluffy anatomy is adaptive, and forces its way into other Fluffy flesh connected to it. Veins grow from the living flesh into the dead, and some kinda organelle in the blood cells rejuvenates dead cells or something so long as it hasn’t reached a certain level of decomposition. Or something, I dunno.
You just have to be careful to match it up. Feel the bones under the hoofpad for left and right legs, and be aware of how to determine if its front or back. Or not! Create a fucked up flesh golem that’s just happy to have sensation and mobility again.