You're right, my bad, neither of them is recommended by the HRN.
I know I will sound heretical now, but I don't see that much advantage in having a surgeon perform all, or some, steps of HT. First, I'd rather have more qualified persons doing the work to avoid fatigue, and second, the anatomy of HT is pretty basic and I think a well-trained technician is as good as a doctor. That said, a surgeon must be present at all times, of course.