[Phantom]

To solutions that I can think of to try for attaching the shade cloth are:

1. Use 4-6 strong magnets on both sides of the glass. Alternatively you could epoxy a few metal tabs to the window frame for the magnets to stick to. This might not work if you get strong winds.

2. Install some kind of pin/hook on the outside of the skylight frame. Sow heavy elastic bands doubled up at the corners of the screen and add eyelets at the end. Attach the screen to the eyelets so the screen will be pulled tight. With some testing you might be able to have enough slack to allow the skylight to still be opened and have the screen inplace.