You also have top take into account the orbits of Jupiter and Saturn; to close to them will pull you way off course. Or can you “slingshot” off of them with a properly timed burn?
to take...too close...
more coffee
You would have to account for any planet that the probe might approach, but I am not sure that the probe actually got anywhere near any other bodies. And certainly the probe can do a slingshot maneuver if it engages in the proper burn near a planet. My point though was that there’s nothing particularly amazing or difficult about getting a probe into an orbit that will closely approach Pluto. Once the proper orbit is achieved it’s just a matter of time until the probe inevitably gets to its destination.
That’s exactly what New Horizons did, flying by Jupiter in February 2007 to pick up speed. Otherwise, the journey would have been even longer.