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I had lumpectomy. Before I left my room in the hospital for the operating theatre, the nurse handed me a surgical hat. In the operating theatre, every medical staff wears a surgical hat. I only removed my hat after I returned to my room after the surgery. I suppose it's a must to wear a hat.
Regarding dignity, well, I too don't have much left. You are not alone.
I will pray for you every success with your mastectomy and reconstruction.