Small space debris objects of even a few centimeters can cause severe damage to satellites. Powerful lasers are often proposed for pushing small debris by laser-ablative recoil toward an orbit where atmospheric burn-up yields their remediation. We analyze whether laser-ablative momentum generation is safe and reliable concerning predictability of momentum and accumulation of heat at the target. With hydrodynamic simulations on laser ablation of aluminum as the prevalent debris material, we study laser parameter dependencies of thermomechanical coupling. The results serve as configuration for raytracing-based Monte Carlo simulations on imparted momentum and heat of randomly shaped fragments within a Gaussian laser spot. Orbit modification and heating are analyzed exemplarily under repetitive laser irradiation. Short wavelengths are advantageous, yielding momentum coupling up to ∼40  mNs  /  kJ, and thermal coupling can be minimized to 7% of the pulse energy using short-laser pulses. Random target orientation yields a momentum uncertainty of 86% and the thrust angle exhibits 40% scatter around 45 deg. Moreover, laser pointing errors at least redouble the uncertainty in momentum prediction. Due to heat accumulation of a few Kelvin per pulse, their number is restricted to allow for intermediate cooldown. Momentum scatter requires a sound collision analysis for conceivable trajectory modifications.