The outcome of collisions between small icy bodies, such as Kuiper belt objects, is poorly understood and yet a critical component of the evolution of the trans-Neptunian region. The expected physical properties of outer solar system materials (high porosity, mixed ice-rock composition, and low material strength) pose significant computational challenges. We present results from catastrophic small body collisions using a new hybrid hydrocode to $N$-body code computational technique. This method allows detailed modeling of shock propagation and material modification as well as gravitational reaccumulation. Here, we consider a wide range of material strengths to span the possible range of Kuiper belt objects. We find that the shear strength of the target is important in determining the collision outcome for 2 to 50-km radius bodies, which are traditionally thought to be in a pure gravity regime. The catastrophic disruption and dispersal criteria, $Q_D^*$, can vary by up to a factor of three between strong crystalline and weak aggregate materials. The material within the largest reaccumulated remnants experiences a wide range of shock pressures. The dispersal and reaccumulation process results in the material on the surfaces of the largest remnants having experienced a wider range of shock pressures compared to material in the interior. Hence, depending on the initial structure and composition, the surface materials on large, reaccumulated bodies in the outer solar system may exhibit complex spectral and albedo variations. Finally, we present revised catastrophic disruption criteria for a range of impact velocities and material strengths for outer solar system bodies.