I did it last winter and I'm nearly 60.
MY shorts are quite wide, knee-length and cuffed, and I wore them over tights and knee-high boots with a blazer, beret and long scarf etc. I was attending my teenage son's school concert, and the next day he told me that some of his female friends had remarked that they liked my outfit. Teenagers are the toughest critics of all, so I reckon if I can pull it off, so can you. Wear shorts that are modest, fit you properly and are a flattering style to start off with, and you are probably showing no more actual leg than the woman next to you who is wearing a skirt - even less if you wear long boots!