How Long Would This Experiment Take?
The light signal from the probe travels at the speed of light, which is the ultimate speed limit. The probe must travel much slower, so the time for a light signal to travel to Cyg X-1 and back is a measure of the absolute minimum time this experiment could take. It is an easy matter to calculate this minimum time, once you know the distance to Cyg X-1.
The total distance traveled would be twice the distance to Cyg X-1.