The aircraft could fly empty to arrive at airports near outbreak areas, then be used as a hospital after it arrives and the pilot disembarks. Once the hospitals in the area gain some ability to control the outbreak, remaining patients can be sent to local hospitals, the aircraft can be decontaminated and left to sit for some period of time, and the aircraft can move to the next region.
If it were truly necessary, you could also set up an airtight septum to separate the contaminated part of the aircraft from the front part that includes the cockpit. There is an aft door (as well as emergency exits) that can be used to access the rear of the aircraft.
We public know what the issues was. Apart from MCAS risk, I think the planes would be mostly safe for these one-off missions.
It just has to fly handful times, from Boeing park lots to a depot in a desert and back from frontline after months/years. They are supposed to be clean before deployment, and can be cleaned by medical professionals before reflying. Or maybe cracks would develop and can't be manned after anyway, either way not much there is in terms of infection risks.
Take out the seats, equip the cabin with ventilators, and when one outbreak gets under control, send the aircraft to the next outbreak zone.
They even have their own generators lol.