It took about a week or so for the scab from the first round of treatment to come off. At that point the spot looked pretty normal, however I noticed there was a tiny hard spot under the skin. I wasn't sure whether it was just scar tissue or whether it was a few cells that were missed by the treatment. So decided to try a few more treatments.
I was very careful to get the plant sap only on what I thought might be affected cells. This time the first treatment yielded no sensation, no tickling, pricking or tingling at all. and after 24 hours it looked like this.
Here comes the disclaimer. This was a personal experiment. I am not telling you that if you use petty spurge on your skin cancer that you will be healed. The sap is reported to be very caustic and can cause serious damage to healthy skin AND all parts of the plant are toxic if taken internally. I was taking a risk using it so close to my mouth, and if you decide to conduct your own personal experiment do not use petty spurge on or very close to your eyes! It can do serious damage to eye tissue.
In the meantime, do your skin a favor and protect it from the sun. Wear big hats in summer, wear long sleeves even when it's nasty hot if you're going to be in the sun, buy UV protective clothing. The sun's rays seem to be getting stronger and stronger and so we are at continually greater risk of contracting skin cancers and other skin abnormalities like actinic keratosis.
Take care of yourselves and be healthy!