For breast cancer, should we do chemo first or surgery?

Hi doctor,

My grandmother was diagnosed with breast cancer three years ago and had a right mastectomy. She however did not have chemo or radiation. She has a little extra fat on the lateral area of the breast that after surgery it looked like a small third breast. Right over the old incision, a large ulcerative cauliflower-like wound has developed. The tumor is protruding and is very vascular. It currently has no odor, but it is bright red and bleeds excessively once the dressing is removed. She is 86 years old with a history of high blood pressure, COPD, CHF, diabetes, CAD, TIA, and pacemaker. She still ambulates, is alert and oriented. Also, she understands what is going on. We visited the oncologist and were told she will either need to undergo chemo or radiation. The surgeon, who did the mastectomy, is recommending surgery to remove the protruding tumor. Which is the best option to do first? My family is very leery about her ability to handle chemo and frankly does not want her to have chemo. We know that removing it does not cure the cancer. Should we do radiation first then remove it with surgery? If we were to consider chemo should we do some cycles first and then remove it with surgery? Which option would you say is the safest route? We want to keep her around for many more years if we can. Thanks for your time.