Sometimes seeing educational cartoon diagrams and animations too much can mess up our physical intuition.
Try this: a man-made satellite is about as big as a car. The Earth contains all the cars, machines, skyscrapers, cities, Egyptian pyramids, mountains, glaciers, all the oceans and continents, including all the countries and histories you've ever seen or heard of. Everything just mentioned is on the surface of the Earth's crust – which is under 1% of the mass of the whole planet. And Earth is one of the smaller planets.
This isn't a direct answer, but an invitation to recalibrate your mental model of the Solar System in comparison to everyday things. But I think the planetary orbits are safe from our machinations. What is of modest concern however, is biological contamination of ecosystems (either artificial introduction of life to a viable world, or the wiping out of a fragile existing ecosystem by an "invasive" Earth microbe). Space agencies take some pains to prevent this.