Nagini is not dead. She is a living creature.
“I don’t think so,” said Dumbledore. “I think I know what the sixth Horcrux is. I wonder what you will say when I confess that I have been curious for a while about the behavior of the snake, Nagini?”
“The snake?” said Harry, startled. “You can use animals as Horcruxes?”
“Well, it is inadvisable to do so,” said Dumbledore, “because to confide a part of your soul to something that can think and move for itself is obviously a very risky business. However, if my calculations are correct, Voldemort was still at least one Horcrux short of his goal of six when he entered your parents’ house with the intention of killing you. He seems to have reserved the process of making Horcruxes for particularly significant deaths. You would certainly have been
that. He believed that in killing you, he was destroying the danger the prophecy had outlined. He believed he was making himself invincible. I am sure that he was intending to make his final Horcrux with your death. As we know, he failed. After an interval of some years, however, he used Nagini to kill an old Muggle man, and it might then have occurred to him to turn her into his last Horcrux.”
Harry Potter and the Half-Blood Prince, Chapter 23, Horcruxes
Voldemort did not create Nagini with his wand, Nagini was alive when she first met Voldemort. So Prior Incantatem will not show her shadow. The hand was created with his wand, thats the reason it appears.
“Harry’s wand and Voldemorts wand share cores. Each of them contains a feather from the tail of the same phoenix. This phoenix, in fact,” he added, and he pointed at the scarlet-and-gold bird, perching peacefully on Harry’s knee.
“My wand’s feather came from Fawkes?” Harry said, amazed.
“Yes,” said Dumbledore. “Mr. Ollivander wrote to tell me you had bought the second wand, the moment you left his shop four years ago.”
“So what happens when a wand meets its brother?” said Sirius.
“They will not work properly against each other,” said Dumbledore. “If, however, the owners of the wands force the wands to do battle... a very rare effect will take place. One of the wands will force the other to regurgitate spells it has performed - in reverse. The most recent first... and then those which preceded it...”
Harry Potter and the Goblet of Fire, Chapter 36, The Parting of the Ways