Why did Wednesday ask Shadow to hold his vigil?

Question

In the beginning of American Gods, Wednesday includes holding his vigil in the deal with Shadow:

"We haven't made a bargain."
"Sure we have. You work for me. You protect me. You hep me. You transport me from place to place. You investigate, from time to time — go places and ask questions for me. You run errands. In an emergency, but only in an emergency, you hurt people who need to be hurt. In the unlikely event of my death, you will hold my vigil. And in return I shall make sure that your needs are adequately taken care of."
_{American Gods, chapter 2 (emphasis added)}

When Wednesday does

get shot and killed, Shadow does hold his vigil.

In the process,

Shadow dies (but gets better) and discovers what Wednesday's plan was, allowing him and Laura to stop it.

Why did Wednesday ask Shadow to hold his vigil? I don't see that was beneficial in any way to Odin; it only lead to

him getting found out and stopped.

Why didn't he have, say, a dwarf hold the vigil like Czernobog suggested? Why specifically Shadow?

Answer 1

The vigil was supposed to result in Shadow's death, dedicated to Odin/Wednesday.

This is mentioned briefly in the all-too-brief conversation between Shadow, Wednesday, and Mr World in which the real plot of the war emerges. Firstly, just as Shadow enters the cave:

A voice from behind him, in the shadows, said, very quietly, “You have never disappointed me.”

Shadow did not turn. “That’s weird,” he said. “I disappointed myself all the way. Every time.”

“Not at all,” said the voice. “You did everything you were intended to do, and more. You took everybody’s attention, so they never looked at the hand with the coin in it. It’s called misdirection. And there’s power in the sacrifice of a son—power enough, and more than enough, to get the whole ball rolling. To tell the truth, I’m proud of you.”

“It was crooked,” said Shadow. “All of it. None of it was for real. It was just a setup for a massacre.”

“Exactly,” said Wednesday’s voice from the shadows. “It was crooked. But it was the only game in town.”

Then, after Shadow reveals that he's understood the name of the game and it was all a "two-man con":

He thought he could see Wednesday, now. He was a shape made of darkness, who became more real only when Shadow looked away from him, taking shape in his peripheral vision. “I feed on death that is dedicated,to me,” said Wednesday.

“Like my death on the tree,” said Shadow.

“That,” said Wednesday, “was special.”

I'm not sure if Shadow coming back from the dead was part of the deal or not: if he was supposed to just die there, or die and come back without understanding the plot, or even die and come back understanding the plot and then either join forces with them or be destroyed by them. But certainly the purpose of the vigil was for his death, the sacrifice of a son for his father, to give power to Mr Wednesday and allow him to come back, at least in some form, even before the battle began.

Don't forget the role of Laura. She messed up their plan perhaps even more than Shadow did. If not for her, they might have been able to keep him in the cave, stop him from going out to warn the other gods until the battle was underway and unstoppable. It all very nearly worked out as they planned.