Should be able to take down to the exterior boxes w/o disturbing the
inside and reflash as a new installation would have been.

I would not recommend leaving old flashing and roof and trying to do
something over the top of that; that's just asking for trouble down the
road.

That was my next question: are the skylights attached only to the
roof, or are they attached to the ceiling joists inside?
If I can remove the skylights without disturbing the inside sheetrock,
that would be great.