Assuming the subject doesn't want to get his head chopped off, then you're no longer asking the question "what does decision theory say you should do", you're asking "what does decision theory say you should do, given that certain types of analysis to determine what decision is the best are not allowed". Such a question may provide an incentive for the person sitting there in front of a homicidal computer, but doesn't really illuminate decision theory much.

Also, the human can't avoid getting his head chopped off by saying "I'll just not make any decisions that trigger the halting problem"--trying to determine if a line of reasoning will trigger the halting problem would itself trigger the halting problem. You can't think of this as "either the human answers in a split second, or he knows he's doing something that won't produce an answer".

(Of course, the human could say "I'll just not make any decisions that are even close to the halting problem", and avoid triggering the halting problem by also avoiding a big halo of other analyses around it. If he does that, then my first objection is even worse.)