One thing which isn't exercise, but could help as well is to use a small packpack instead of a handbag. If you usually hang a shoulder bag on one shoulder (with all the mountains of stuff in it that you just might need), you have to hunch that shoulder slightly to stop it falling off.
A backpack has a strap round the front of each shoulder and the weight is at the centre of your back, so the more that is in it, the more it pulls your shoulders back. You can get a small amount of shopping in it, or essentials for a day out, and of course a bigger one will take more, some as much as a suitcase will.
I am a great fan of them, and hardly ever use a traditional style of handbag these days. I have no car, so have to carry home any shopping up a hill. A heavy bag in one hand makes my shoulder ache, but carried on my back the same amount of stuff feels lighter, and I have both hands free for opening doors and so on. There is an amazing variety out there - you don't have to look as though you are setting off to trek to Timbuctoo. A page of images