How significant are the recent results that Scholz’s Star has perturbed several observed hyperbolic objects?
Not an answer, but just on radiants:

Radiant means angle of approach.   It's applied to meteor showers because the Earth intersects the dust trail that causes the meteor shower at a specific place in orbit and dust trail has a specific angle of intersection relative to Earth and Earth's orbit.  



Source of picture.


  What is the "radiant" of a minor body with a hyperbolic orbit in a
  simulation


Radiant can't be applied to elliptical orbits though extremely elliptical orbits kind of have a radiant, but it can be applied to objects approaching the solar system.  A hyperbolic orbit generally implies an object that came from outside the solar-system though it could also be a gravity assisted object from inside the solar system that was accelerated from an elliptical to a hyperbolic orbit.

Here's an article that mentions radiant in association with an exo-solar object


  astronomers looked for the radiant it seemed to originate from.
  Calculations determined that A/2017 U1 came from a radiant located
  close to (R.A. = 18h 41m 25s ; Dec=+34° 15′) coordinates, which is
  near the actual position of Vega


exo-solar objects approach the solar system in a mostly straight line until they get close enough for the sun to bend their path.   Where they came from before their direction was curved by the sun's gravity is their radiant.