Appearance Issue of Assisting a Blind Woman?

I work together with a blind woman who my boss considers a valuable asset to the company. Until recently, she got rides to and from work from another coworker who was female. That coworker retired last week. This leaves me as the only one who can provide her transportation, and my boss specifically asked me to drive her to and from work as if it’s now part of my job description. Where we work, it is necessary to park two blocks away from the office and walk several minutes down the street. The blind woman has to walk with me and hold on to my arm as I walk to and from the car and to guide her.

For the first few days, all was fine. Then an acquaintance of mine who knows I am married but has never met my wife saw me and emailed me and told me that he saw me walking together with my wife. He assumed this woman was my wife because it appeared she was clinging to me in a romantic way. I explained she was not my wife, but a blind woman I am assisting. I have been married to the same woman for over 30 years. My wife very much supports me helping a blind woman because she considers it a chesed. The blind woman also is married and her husband is appreciative of anyone who helps her.

There is no negiah issue here because this woman does not make contact with my body, but she holds my loose fitting jacket with one of her hands. She only touches the fabric, away from my body, and not my skin. I don’t even feel her. But I am wondering, is there an problem in Jewish law if to the eyes of others, it gives the mistaken impression we are romantically involved?