Basal and squamous cell carcinomas develop very slowly--months at a minimum, years more commonly. The recent onset is very reassuring. Biopsies do not spread cancer. Punch biopsies give more information, since a superficial shave might miss deeper pathology. In your situtation, it sounds like your dermatologist is exactly right in his approach. By the way, I advise leaving the area alone (no rubbing or close examination) since trauma might confuse the issue and force a biopsy when you could get away without one.
Overall, though, you should relax--4-month followups for your condition are more than adequate to head off any trouble.
Best.
Dr. Rockoff