I should have made it even clearer that there is no desire for the RH pilot (the one with the IR) to log anything whatsoever.
This isn't the standard question that keeps coming up, asking if both can log it.
I think it was recently established that it is legal to do something similar in VMC. The LH pilot can fly under the hood, while the RH pilot can be a safety pilot. Both can be plain PPLs. The LH pilot can log this as "simulated instrument time" and this will count towards the main FAA IR instrument time requirement.