Manuals are generally silent on the matter, so a "mild" non-normal results in the standard roles for Pilot Not Flying (PNF) on the radio and Pilot Flying (PF), with both operating switches in their area of responsibility.
Commander can always direct otherwise, though, so in a "major" non-normal, where the commander becomes the PF either by direction or automatically, and with a requirement for faster action than directing radio comments through the PNF can achieve, I personally would physically fly the aircraft AND liaise with ATC through the radio, and direct the PNF to read & do the QNH.
As, for instance, occurred in the Hudson ditching.