I have never seen a duck punt on Chichester Harbour, but as they go out before dawn and at low tide in winter this is hardly surprising. Wildfowlers are clearly a hardy breed, innured to long periods lying doggo in a small boat in the bitter cold, waiting for their chance. There is a delightful account of a duck hunt by Allen Musselwhite here (scroll down to 'A morning in the punt').
All the piece lacks is some pictures, so for an idea of what modern duck punts looks like, go to the Domeyer Scull Boats site in the US, which has some evocative photos of early morning mists on the river.The site is a veritable encyclopedia of duck hunting and how to do it, especially the art of sculling with an oar out the back. The hunter lies on his back with his right arm over his chest, holding the oar over his left shoulder and waggling it in a figure of eight motion to move the boat stealthily forward towards the target.
Interestingly, the hunters seem to use regular shotguns rather than the traditional duck gun that Musselwhite describes, a monster weapon fixed to the punt so the boat has to be steered accurately into place before firing.
Selway Fisher do plans for a couple of duck punts for home construction, but they are really for rowing and fishing rather than hunting.