I would most definitely recommend Close Combat. It's a very powerful attack, and you're lacking a Fighting STAB attack. Unfortunately it doesn't get the bonus damage from Iron Fist, but it's still strong, especially if it's boosted by Life Orb or Choice Band. The defence drops are not that important because Infernape isn't meant to be tanking hits anyways.
If you're going to be running a choice item but still want priority, Mach Punch is a good alternative to Fake Out. You lose out on the flinch, but it's STAB and gets boosted by Iron Fist, so it's not a terrible move to be locked into.
If you do end up using Infernape in doubles, forget Mach Punch and Choice Items, and keep Fake Out. Fake Out is a very strong move in Doubles because it gives your partner a chance to use a boosting move in relative safety, or take out an immediate threat before they can do any damage. I used Fake Out strats a lot when I played VGC doubles.
I hope this answers your question, and if you have any questions/suggestions please give them :)
