Hi Kazcook,
I haven't had radiation but I have had outpatient surgery on my back and on my head for non-melanoma skin cancer, with local anesthetic injected around the occurrences beforehand. The surgery wasn't particularly painful and I found the procedure quite interesting. Personally I'd prefer outpatient surgery rather than radiation because radiation might take several sessions and produce painful side-effects and has small risks of radiation damage associated with it. Freezing the affected area with dry ice is another option for some people. I've had a small mole removed by the freezing technique and that was very simple and I don't remember any pain associated with it. But it might involve several visits to get a large area done or they may feel your carcinoma is too big and well-developed for that kind of treatment.
You can read about basal cell carcinoma and its treatment options on the internet eg here http://www.skincancer.org/skin-cancer-information/basal-cell-carcinoma and there are more links here http://bestcancersites.com/skin/ .
Good luck whatever option you choose 🙂
Ed.