Some Connecticut allow firearms deer hunting too. I have hunted Pattaconk State Park on A Season shotgun and blackpowder tags before.
I wouldn't be too worried about hiking when the hunters are on the prowl. I would recommend wearing an orange vest (and other visible clothing) and calling yourself out when you come upon a hunter, so they know you are there. When I'm stalk hunting, I do that when I notice a stand hunter. I have also interacted with mountain bikers and families hiking while hunting- I try to let them know my plan, and get an idea of where they'll be, so I can avoid shooting in their direction.
Another thing- I'm not sure about down there, but it seems like there is often quite a few more hunters out and about on weekends than during the work week. And, if Sundays are a no-hunting day in your state- use that to your advantage.
