I had cryotherapy done for my eye wart. It only took a few minutes and the wart fell off after a few days. It wasn't painful either. I highly recommend this procedure.
If the wart was on my hand or arm, I would have tried to treat it at home. But I agree that the eye is very important and the eye area is sensitive. So I decided to get cryotherapy which my doctor suggested.
There isn't a scar, there is just a slight discoloration if I look closely in the mirror. I don't think that's a big deal though. Overall, I'm happy that I got it done.