I think/presume that you are looking for a 4" / 100mm Grill vent that you can manually open and close. in the 4" hole But I have never seen one of these. Presumable because manufacturers thin that you would never have a fan infront of a closer that you could manually close when fan was on (perhaps overheating the fan).
Nice looking product.
But I expect it is not suitable for OP without some modification to his Vent pipe, as it has a 102mm outer diameter, and so the screw holes will fall inside his 4"/102mm diameter vent pipe.