Turn down/off any oxygen around the patient's face before the surgeon uses the cautery. The most stimulating part will be the local injection around the eyelid. Make sure to have a little extra propofol onboard. After that, its just keeping the patient motionless while the surgeon cauterizes and sutures. This is easily achieved by periodic small doses of propofol.
The problem here is that the lower eyelid is turning outward. This is called an ectropion eyelid. The surgery is to correct this.