If its any help we've kept a few hams in converted rabbit hutches now. Scamp and Fwirl (their first inhabitants) never chewed the wood at all. Muddle is in one now and he's only ever chewed a tiny bit - that was easily stopped. The fourth ham to occupy a hutch was Eggbiscuit and we learnt a lesson about not keeping really, really destructive hams in anything thats not either glass or metal lol
I think chances are that your ham will behave itself