Geosynchronous orbits do not pass through the Earth's shadow as much as you might think. These orbits sit in the same plane as the equator, which is tilted 23.5 degrees when compared to a line from the sun to the earth.

They still pass through the earth's shadow in the weeks around the equinoxes though. Worst case is about 70 minutes of shadow.

That said, it seems more likely to me that there is no requirement to stay over the same spot on the earth, and a lower altitude sun-synchronous orbit would be used.