My Mother died from breast cancer and as your sister feels very private about it so was my mother. Cancer was never mentioned in our home. Nor would she listen to the oncolgist Istay in the room to hear what was going on while Mom left and got dressed. I too am 13 years breast cancer free.I'm open on talking on it , which I just did at Relay For Life which covers all cancers.
If your sister is that private about it, I would not put the pink ribbon fabric on the back. My opinion only