You might lose a few peppers, but you'll get far more growth and many more peppers in return. Peppers are pretty tough.

Are you sure it was meant to be edible, or was it just sold as ornamental? I ask because sometimes ornamental peppers sold as ornamentals have systemic poison in them. If you want cayenne peppers, I'd just to go a big box store and buy a plant in the veggie section. They grow so fast.

This was meant to be an edible. This was a huge festival of garden growers and lovers and thousands of plants were for sale. I just happened to get a healthy looking pepper in a hanging basket.

I'm not an expert with peppers, but I've transplanted them this time of year when I lived down in 9b, and as long as you keep them watered, they should be fine. The leaves might burn a little, because you don't know how that was grown. Put it somewhere that it can grow to its heart's content, because they get big. Also, cayenne is a tender short-lived perennial in your neck of the woods. If you protect it from freezes and keep it happy, it will live for from 3 to 5 years. Eggplants are like that too. I had a Japanese eggplant that lived for 3 years and got almost as tall as me!