I'm writing a sci-fi book where the main method of travel involves collapsing a star into a black hole by putting a satellite equipped with some sort of handwaving mechanism into orbit around the star. The satellite can then direct a beam of energy with a cross-sectional area the size of the black hole itself (ex. our Sun's Schwarzchild radius is just shy of three kilometers, so that would be the radius of the beam created out of a black hole from the Sun).
Once the spacecraft enters the beam, it enters a "free-fall" accelerating at about 51 G, to a maximum speed of about 10 000 c. The satellite can send messages to the spacecraft instantaneously at any point along the beam, but the spacecraft can't communicate back - only receive. A property of this beam that I'm bringing into the story is that the process of traversing the boundary in or out triggers a massive EMP that fries anything electronic on-board. The satellite observes the EMP from its orbit and calculates the time at which the spacecraft must exit the beam to reach the next system, and communicates this to them. Because of this, the engineers on-board the ship have to repair the communications array after every entry and exit of the beam. For the same reason, physical mechanisms for basic things like life support, lighting, etc. are highly preferred. Transit time in the beam (and therefore maximum time to fix the communications array) varies, but would typically be a month or so at most.
My question is whether, after leaving the beam in the new star system probably up to as far as a few AU away from the star, what would be the bare minimum of electronic components related to the calculations needed to plan the burn length, timing, thrust, etc. and control for these mechanisms that would need to be repaired/replaced to be able to accurately deploy the satellite into a near-zero-eccentricity orbit within 0.1 AU? Bear in mind that these missions are decades long with dozens if not hundreds of jumps, and new resources would need to be acquired from each successive system (ex. chemical rocket fuel extracted from a gas giant or from the star itself prior to collapsing it, minerals from asteroids or rocky planets, etc.).
EDIT: Have accepted an answer from @Starfish Prime, but received lots of good suggestions in comments as well. I am now aware of the issue with EMPs injuring humans as well, so will be modifying the mechanism accordingly.