One does not simply fight without headgear, just one week before the fight expecting not to be cut. That cut, fake or not, is fully intentional, and not even that surprising, coming from a compulsive liar like Haye is.
Why would he do that though? Haye stands to make a lot of money and Haye is also the clear favourite. It's not the same sparring/fighting with or without head gear especially when training to slip punches (vision impared and head larger with headgear). Haye needed a different gameplan then the Chisora or Wlad fight, a game plan that probably involved slipping Fury's punches and tagging him. It wouldn't surprise me if Haye was training to slip punches without headgear but got tagged and so ended up with the cut.
not fake, not Haye's fault. Why would be not want to fight Fury? It is big money for him and a fight he should comfortably win that could get him another title shot.
Why did he duck Vitali and went to the jungle? I doubt he could earn there more money than against Vitali.
I don't think he faked it like he has all his other 'injuries' but a 6 stitch cut doesn't need 6 weeks to heal like his is claiming. He wanted out of the fight for some reason and this was his way out.