All you'll need is a white shirt, white pants, and a white wig. You could possibly carry around an action figure or something like that. I've seen a few Near cosplayers carry around Transformers action figures, or you could re-create the lego pieces he uses to represent the people in the story (X-Kira, Kira, Misa, etc.)
"Why do all the Death Note fan-girls choose to fawn over L instead of me?"
"Because, Light, unlike you, L is full of win!"