Preheat the oven to 200 degrees Fahrenheit. Place a metal bowl the same size as the album face down onto a metal baking sheet.
Place a quarter in the middle of the album, centered over the hole in the middle of the record. Trace around the quarter with a pencil. Remove the quarter and cut away the record label inside the circle, removing all traces of paper. Turn over the album and do the same thing on the other side.
Lay the album onto the metal bowl. Place the baking sheet into the oven. Allow the vinyl record to heat and soften for five minutes.
Remove the baking sheet from the oven and set it on a heat-proof surface. Use the screwdriver to stretch the softened vinyl in the center of the album to widen the hole. Make the new hole the same size as the circle you traced from the quarter.
Push and fold the edges of the album down over the bowl to create a round shape. Form the record into a bowl shape with fluted, wavy sides. If you want a smaller shade, turn the bowl over and place the album inside.
Work fast, as the album will cool in a few minutes. If you are not finished molding the record before it starts to harden, place it back into the oven for a couple of minutes to soften it again, then take it out and finish the job.
Thread the light plug through the hole in the center of the shade to complete your hanging vinyl record lamp.