I'm not even sure he'd need a wig ... a different hairstyle might be enough. Along with a bit of makeup.
I don't get where that fellow thinks Bradley is a dead wringer for Hartnell. In those park shots he doesn't look a thing like him. Where I come from, that's called, "might be mistaken for the fellow on dark, foggy night by a witness with no corrective lenses and severe myopia."