You realize you just tore these cores out of rogue AI battleships trying to vaporize you, yes? And you want to put them back into AI battleships?
They seem to be perfectly safe and trustworthy to immediately put in charge of:
My Megaport, through which all my planet's cargo goes.
My Orbital Works, through which my empire's war fleets are outfitted to the tune of what must be dozens of capital ships per month after a while.
My planetary defenses.
My fleets' High Command structure.
The giant space station in orbit that can basically stand off and blow up a fleet all on its own.
Every other industry around which in itself can be abused in less obvious ways to do terrible things.
My planet. Literally in charge of the entire planet and everything on it.
Frankly, it'd make more sense to test them out on a ship in your fleet first.