Would it be okay to have an alcoholic drink before a pap smear?

Yes. If by one drink you mean a standard drink (5 oz. 12% wine, 1 1/2 oz of 40% liquor or 12 oz. Of 5% beer) it should cause no problems. However, having the odor of alcohol on your breath at your doctor's appointment might get noticed. If you are anxious about the exam or any discomfort, discuss that with your doctor. A low dose of a tranquillizer like ativan, (lorazepam) often given by dentists, may help(0.5mg).
Depends on safety. A pap smear takes a sample of cells from the cervix. Cells there don't change quickly, so having an alcoholic drink makes no difference to the cervical cells or pap smear. However, if a patient has to get home by riding a motorcycle, driving a car, or flying her plane after leaving the doctor's office, having a drink would be a bad idea from a safety point of view.