Fast beam collinear laser spectroscopy is the established method to investigate nuclear ground state properties such as the spin, the electromagnetic moments, and the charge radius of exotic nuclei. These are extracted with high precision from atomic observables, i.e., the hyperfine splitting and the isotope shift, which become possible due to a large reduction of the Doppler broadening by compressing the velocity width of the ion beam through electrostatic acceleration. With the advancement of experimental methods and applied devices, e.g., to measure and stabilize the laser frequency, the acceleration potential became the dominant systematic uncertainty contribution. To overcome this, we present a custom-built high-voltage divider, which was developed and tested at the German metrology institute, and a feedback loop that enabled collinear laser spectroscopy to be performed at a 100-kHz level. Furthermore, we describe the impact of field penetration into the laser–ion interaction region. This affects the determined isotope shifts and hyperfine splittings if Doppler tuning is applied, i.e., the ion beam energy is altered instead of scanning the laser frequency. Using different laser frequencies that were referenced to a frequency comb, the field penetration was extracted laser spectroscopically. This allowed us to define an effective scanning potential to still apply the faster and easier Doppler tuning without introducing systematic deviations.