Go HereFor a replacement skylight
The I assume white putty your asking about is Dicor Lap Seal. Pick up a new tube of the same stuff from any RV dealer, go to a big box store and buy a plastic scraper, go home and go to work. The old Dicor will come off with some effort. Once you have the screws uncovered, using your cordless drill remove the screws. Now using the scraper, carefully pull the skylight sway from the roof. Clean up the left over Dicor as best you can. Apply a generous bead of Dicor to the bottom of the new sky light, carefully place it and screw it into place. Finish up by applying a generous amount of new Dicor around the seam and screw heads. Let things dry and your good for another ten years.