How does 'standalone' propeller efficiency change with altitude?
Yes, the same propeller can be used.
Propeller thrust is proportional to air density. The same is true for aerodynamic drag, so your propeller will work at all altitudes equally well. Since the speed of sound drops with temperature, you need to pick your propeller tip speed for the coldest layer, which normally is the Tropopause. There, the speed of sound is 295 m/s and if the propeller tips don't exceed 85% of that, efficiency should be roughly constant over altitude. A small loss in efficiency with altitude must be accepted, however, since the propeller's friction drag increases with altitude.
This would not be true for airplane propellers where the drag of the airplane they are propelling is constant (actually, rises a bit) with altitude, but since your thrust demand drops in line with density, no new propeller is needed at 85,000 ft.