I don't think the term "blowing up" is suitable, for if you create such a force on the surface of the planet, just to "nudge" it off its current orbit, the amount of energy you require would also be sufficient enough to DESTROY the said planet. Which we don't want to happen, yes?
I honestly can't figure out an alternative way to "push" or "nudge" a planet out of its orbit, considering the mass involved. The earth's mass is 5,973,600,000,000,000,000,000,000 kilograms (incidentally, you can also say "nearly six septillion kilograms", or just simply 5.9737 × 10^24 kg). Just think of the energy required to move it out of its orbit considering that it's moving at around 30 kilometers A SECOND through space as it revolves around our sun.
Perhaps one day, creating "mini black holes" at certain points in space near the paths of planets, would be the key to "orbit nudging", but hey I'm just wildly speculating here.
ADDENDUM: I just realized that, you will encounter YET ANOTHER PROBLEM after you've successfully "nudged" a planet out of its current orbit to one with a greater or lesser apogee--circularization. For if the resulting new orbit is highly eccentric, then the planet would swing into that "goldilocks zone" at some time, yet swing out of it some other time, which could be very very bad for the inhabitants of the said planet.
-RODION





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