A black hole may very well give you the acceleration that you need, but there's a lot more to it than just that.
Aiming is going to be an issue for you. Consider the total distance that your electron will travel. You're talking about orbiting a celestial object, so the electron would be traveling for hundreds of millions of kilometers. Firing two infinitesimally small particles at each other from $10^{11}$ meters away and trying to get them to collide will be a stupendously difficult task (like hitting a pop can with a BB gun, except the can is on Mars). A particle accelerator keeps the particles in a controlled environment, using magnetic containment to keep them on track. Yours will be floating free in space, subject to whatever gravitational forces they happen upon. The black hole will be the dominant force but given the sizes and distances that you're working with, something as simple as an asteroid wandering too close can nudge your particle far enough off course to miss the target by kilometers.
Also, a particle accelerator protects the interacting particles with walls that provide physical shielding, plus a vacuum in the interior. We like to say that space is a vacuum but in reality there's a lot of matter floating around out there, not to mention photons, cosmic rays, etc. A flight path of that length will give you plenty of opportunities to collide with a random particle of something else before you reach the destination.
It's a lot of space to have to control in order for the experiment to work. Particle accelerators avoid that problem by making a large number of loops through short, circular tracks (same total flight distance, but less space to control). You're sending your electrons on a long trip through a wild, uncontrolled frontier. It could conceivably work, but I'd wager that the percentage of particles that actually make it to their destination will be low enough that this won't be a feasible system.