You can keep it in the same orbit but spread the mass out along the orbit to the other side and that changes the combined CoG to be closer to Sun's CoG in turn changing Earth's orbit, albeit probably slightly
GPT4 seems to think it is a 3 body problem. Mercury and Earth are of similar size and exert gravitational effects on each other. Take away mercury and maybe the earth slowly drifts a little.
The point is that a very small difference in starting conditions yield wildly different results.