Laser triangulation sensors are one of the most commonly used optical sensors in dimensional metrology and quality control. This article presents a method for simulating the laser speckle-induced measurement uncertainty, representing a major performance limitation of these sensors, as well as the effects of speckle reduction mechanisms based on spatio-temporal averaging. To investigate the relation between triangulation angle and the resulting speckle-induced uncertainty, simulations are performed for three sensor geometries, revealing that a larger angle results not only in a smaller measurement range but also in a reduced influence of laser speckle and a smaller uncertainty. A parameter study on a speckle-reducing moving diffuser mechanism, integrated into the optical sensor path, investigates the achievable improvement for various combinations of motion frequency and amplitude. The accuracy of the simulation results is validated by measurements conducted with an experimental setup, demonstrating good agreement between the measured and simulated uncertainty values with and without the speckle reduction mechanism. It is shown that the diffuser is capable of reducing the resulting speckle-induced measurement uncertainty by up to 63%.