Its safer if you use an orange cutting pad, a Porter Cable polisher and some plastic cleaner, I use both 3M and McGuiars. You can also use either company's scratch remover. I finish it off with the pink Zaino 2 polish. I've never had to use the sandpaper and it takes all of 5 minutes with the PC. I had both the haze and etching and my headlights look better than new. One thing I've noticed. After washing your car dry off the lenses quickly. I think there is a chemical in the water supply that causes the etching. I blow dry my car with a leaf blower and then towel dry whatever is left. I started doing this to cut down on the number of towels I was using to dry my car. I went from 4 or 5 to 1. And yes use only a 100% cotton towel or micro fiber towel.
Pat