Not really. If you stand outside and look at the Sun, you can shield your eye with a nickel. Just put the device in space far enough away and it can be just a few hundred meters on a side, mostly to insure coverage because of the movement of the Sun and the target, which could be hundreds of light years away.
You didn't do the math. I hate it when people spout off nonsense that is so easily shown to be wrong. At 100 ly you're looking at covering a target at least 5.87x1014 miles away. you can cover the sun with a nickel because you hold it close in front of your eye and your eye, the target receptor, is relatively small. BUT you can't get close to your target receptor. to carry out your analogy, if the earth were the target and you were attempting to black out the sun, the equivalent of the shutter at 100,000,000 miles from the sun on a target 100 ly away would be 92,000,000 (distance from earth to sun) times ( 108)/5.87x1014 = 92million times 1.7 times 10-7 or your shutter would have to be about 15 miles from the sun to give the same size on earth that a target 100 ly away would see. in short you need a shutter that would cover the sun at 15 miles from the sun. How much of the sun would that nickel cover if it were only 15 miles from the sun?
Not to mention that your target would be about 200,000,000 miles in diameter (about the diameter of earth's orbit), but that makes the geometry a little more complicated and basically shifts the optimum point where you could get away with the smallest shutter to about 1/3 of the distance between the sun and the target system. Not something that anyone could do.