It might work better if the station created a hyperspace conduit to the star of the system they want to destroy and distabilise that star.

With the amount of damage it does in the film to the base’s own star system the weapon would have a very short shelf life (I can’t remember any reference to the base being moveable from star to star).

The problem with this idea is the fast fall of night on the base-world is meant to be a visual countdown to the firing of the weapon but as Ender says it could be explained by natural means.

It would make more sense visually if we saw the base fire and then saw the target sun shrink and the planets blow up rather than the shrinking star being fuel for the weapon.

I would make it a weapon built on a planet instead of an artificial world. The Empire took decades building the first Death Star with all the resources of a galaxy.
Building an artificial planet like that would be noticed and resource heavy. The First Order want to finish their weapon and destroy the Republic fleet and capital. They would only need the gun for that. All the size gags were a bit silly. It would make more sense if the gun was smaller than the Death Star.