Well, there's behavioral economics. That would remain by definition, since it is the study of how people actually behave, i.e. it does not start from the assumption of a rational actor.

Another part that would remain is the purely descriptive, e.g. the study of how the monetary system actually works.

Finally, it's not so much that the notion of a "rational actor" is entirely flawed, it's just that it's taken much too seriously.