What are the navigation techniques used to handle the aggregated unknown effect of gravity from local and distant matter for the New Horizons space probe when it intercepted Ultima-Thule ?
Essentially none. The flyby of Pluto was very close to a straight line trajectory. See the image below.
Pluto's mass was too small to have any significant effect on New Horizons' trajectory. The effect was observable after the fact, about 6 meters per second $\Delta v$. Since Pluto's mass is several hundred thousand times that of Ultima Thule's, the effect of the flyby on New Horizons' trajectory will be very close to nil and may well not be observable at all.
New Horizons has extremely limited onboard translational guidance, navigation and control capabilities. All maneuvers are planned on Earth and transmitted to New Horizons. The ground systems command New Horizons to orient itself to a specific attitude with respect to the stars and at a specific point in time, fire its thrusters until it attains some commanded $\Delta \vec v$.