I believe they make electronic shades for skylights, have you considered installing these? Like this:

We had mini blinds permanently installed over our skylights. They had a small eye loop installed where the wand would usually be to adjust the blinds open or closed. They could be adjusted with the same super long pole we could use to open the skylights. I really didn't like having to have that long pole in the corner of the room but there was no where else for it since they didn't think to make it adjustable so we could put it into the closet. This was a 20' ceiling in our family room. With the skylights open but the blinds closed, we wouldn't get the sunlight but create a draft for the hot air to go out. Kept our family room cool even in the hottest summer weather and it was on the south side of the house!