If the ball is in bounds and is sitting behind a stake that marks a lateral water hazard and isn't touching it, what is the call? Can you move the stake?

You may move them. In the definition of a Lateral Water Hazard it says, "Stakes used to define the margin or identify a lateral water hazard are obstructions."

EDIT: BTW, even if the ball is touching/in the hazard, you would still be able to move the stake.

Be careful. There may be a Local Rule declaring hazard stakes to be Immovable Obstructions. In addition you may only move them if they can be moved without unreasonable effort, causing damage or delaying play.