Did you resolve this dilemma? I think you should talk to your wife about your urges. You don't have to say you cheat, but attraction is not a choice. Communicate with her about it and if the marriage is meant to last, she will make accommodations for your needs.
I am in the opposite scenario. My boyfriend knows I am bi. Right now I don't have the urge to sleep with a woman, but if that happens I've promised him if talk to him, and he said that it love is strong enough that he'd be ok with that. He just doesn't want me to lie to him or hide something... And I won't.