Ciao! I'm assuming you'll have your own car, right? You can most certainly head to The Mall in the morning and shop to your heart's content, then head into Chianti for a visit at a winery and dinner.
You want to see the Black Rooster? There is one in Greve in Chianti, on Via Cesare Battisti - not in the main piazza. It is near the car parking lot. I've seen a temporary one in the piazza so cannot say when it is there or not.
There is also another in Gaiole in Chianti and another in Castellina in Chianti. I am not sure about Radda or Panzano, I've seen them during temporary events.
Do you want the dinner to be at the vineyard? You might want to take a look at the Chianti Classico Card -
https://card.chianticlassico.com/en/experiences?categorie=1&comuni=&filtriComuni=&galletti=0&titolo=
it offers for set prices wine tastings, winery visits, and a few even offer picnic in the vineyards (if you're done shopping by then). Take a look, it could be nice for the wine tasting. For the dinner, I would just recommend once you've chosen the winery to stay there if they have a restaurant or to go to a nearby town. Many places are lovely in the evening, especially those in the countryside with views. You can dine in Radda, to give you an idea of distance, and that's about an hour drive back to Florence. Gaiole is just about 10 minutes more, if you take the A1. So you pretty much have lots of choices, depends on what you're looking for - wine tasting, vineyards, winery + dinner or all separate? Just wine tasting?