Consider this. Pluto was discovered far after the other planets. The reason? Because it's gravitational impact on the rest of the Solar System was so insignificant that we didn't ever consider that there might be another planet.
So, were that planet to disappear, the impact on the rest of the solar system would be nil. However, nothing just disappears. The explosion itelf may harm the solar system in some way, right? Very unlikely. The distance between Pluto and any other planet is always huge, and space is very big. The odds of any of the debris going very far is also nil. It would just end up as a tiny asteroid belt at best, not affecting the rest of the solar system.
As for the death of one planet affecting the entire Milky Way galaxy...
No. The explosion of our sun wouldn't be a blip for the galaxy. One planet is a joke.