I'd get some drywall corner moulding and finish the raw drywall edge that way and leave the rest open to get air. (You also need some joint compound, some sanding sponge and paint. ) I cannot see it clearly enough if it would need some support behind it. Normally drywall is just brought up to the edge of it and it is trimmed out with a small piece of moulding. It looks like the wall and edge of the skylight are not on the same plane so that would not work to bring the drywall up to the edge of the skylight.

What the contractor left you with was just plain sloppy. If it were me, I'd cut away the stuff at the top that is curving inward so that it's all in one plane. Then I'd take some simple wood molding, like 1/2" X 2", nail it in place, and paint it to match. It will be innocuous and look finished.

I would like to see how to fix this. Oh, what a mess I have right now Roofing company is replacing them not sure what to do with the mess inside from replaced skylights