For anyone else who was intrigued by this, I found this helpful animation:
Following this animation I'm left thinking that you could do a bit of filtering to better extract the wave(s) from an image, though you'd require a particular setup for the lighting conditions to get the best possible quality out of it. And then back to my first idea: probably a laser-tip would be the best tool here too.
Unfortunately I don't have vinyl records around to test any of this!