Summary is no for Jupiter, even the entire planet Earth wouldn't affect it that much. Mercury is much smaller though, so it might be possible to make a significant change, though you're probably still talking about sending a significant fraction of the mass of the whole planet Earth.
You might be able to alter the orbit like that without destroying the Earth if you figure out how to gather a ton of mass already in space, asteroids or something maybe. But now you've got to figure out how to redirect their orbit into the exactly right one without throwing most of their mass around, and do it with a reasonably-sized mission from Earth.
Summary is no for Jupiter, even the entire planet Earth wouldn't affect it that much. Mercury is much smaller though, so it might be possible to make a significant change, though you're probably still talking about sending a significant fraction of the mass of the whole planet Earth.
You might be able to alter the orbit like that without destroying the Earth if you figure out how to gather a ton of mass already in space, asteroids or something maybe. But now you've got to figure out how to redirect their orbit into the exactly right one without throwing most of their mass around, and do it with a reasonably-sized mission from Earth.