@bunnyknight
The effects seems to me would be the same if a real star the same mass came within 200 AU of Earth, basically not much. It has been shown dynamically the two closest stars of the Alpha Cenauri trinary that planets could be in stable orbits even though the stars themselves are about as close as Uranus, a LOT closer than 200 AU.
I think maybe you picked a number you thought really close, one light day.
So 24 hours and light flys at around 670 million miles an hour so about 175 AU which is about 4 times further than Pluto.
As for changing Earth's orbit, at that distance it would represent a gravitational field on Earth about 1/30,000ths of the sun. So the sun having 30,000 times more attraction than our reputed star would mean very little change in our orbit, certainly not enough to have Earth fly off the handle so to speak and get shot out of the solar system or some such. I would think mainly there would be small changes in tides once a year when Earth was on closest to the star, similar to the tides that happen from the sun but a LOT smaller. Don't see much happening to Earth orbit.
Just intuitively, it looks to me like a sun size star at 175 AU would have about the same gravitation effects as Jupiter which is roughly a half billion miles or roughly 33 times closer than that star and I would think, as it clocks in about 1/1000th the mass of the star the gravity would be pretty much the same.
The gist of that is we have been living with Jupiter for billions of years now, Earth has that is, and has been hit by fairly large asteroids maybe once every 100 miillion years or so, last big one 66 million years ago.
Don't see that changing much since any perturbation of objects in the Kuiper belt could sling stuff our way but like Humy said, the solar system is pretty vast and it would be a statistical game of very low proportions that one of those objects would crash into Earth. Don't forget, if stuff was perturbed inwards it would have to go by the gravity of Jupiter and that would make Jupiter more of a target than Earth. And there are other large planets out there, Saturn, Uranus, Neptune, so such incoming stuff would have to get by all their gravity fields to get inside to the inner system.