Laser plasma thrusters are a new kind of propulsion system for small satellites, and work with the thrust created by the laser ablation of a target. Liquid polymer solutions are very promising fuels for such systems, provided that no splashing of the target occurs, because ejection of droplets strongly decreases the performances of the system. We have investigated the nanosecond infrared laser ablation of glycidyl azide polymer solutions containing carbon nanoparticles as absorber. Shadowgraphy imaging revealed two cases, namely splashing regime and solid-like behavior. The transition between both regimes depends on the viscosity of the solution and on the laser fluence, and is explained by the recoil force acting on the target. Appropriate conditions to avoid splashing were identified, showing that this liquid polymer solution is a suitable fuel for laser plasma thrusters.