The purpose of this study was to compare the radiation-induced second cancer risks for in-field and out-of-field organs and tissues for pencil beam scanning (PBS) and passive scattering proton therapy (PPT) and assess the impact of adding patient-specific apertures to sharpen the penumbra in pencil beam scanning for pediatric brain tumor patients. Five proton therapy plans were created for each of three pediatric patients using PPT as well as PBS with two spot sizes (average sigma of ~17 mm and ~8 mm at isocenter) and choice of patient-specific apertures. The lifetime attributable second malignancy risks for both in-field and out-of-field tissues and organs were compared among five delivery techniques. The risk for in-field tissues was calculated using the organ equivalent dose, which is determined by the dose volume histogram. For out-of-field organs, the organ-specific dose equivalent from secondary neutrons was calculated using Monte Carlo and anthropomorphic pediatric phantoms. We find that either for small spot size PBS or for large spot size PBS, a patient-specific aperture reduces the in-field cancer risk to values lower than that for PPT. The reduction for large spot sizes (on average 43%) is larger than for small spot sizes (on average 21%). For out-of-field organs, the risk varies only marginally by employing a patient-specific aperture (on average from -2% to 16% with increasing distance from the tumor), but is still one to two orders of magnitude lower than that for PPT. In conclusion, when pencil beam spot sizes are large, the addition of apertures to sharpen the penumbra decreases the in-field radiation-induced secondary cancer risk. There is a slight increase in out-of-field cancer risk as a result of neutron scatter from the aperture, but this risk is by far outweighed by the in-field risk benefit from using an aperture with a large PBS spot size. In general, the risk for developing a second malignancy in out-of-field organs for PBS remains much lower compared to PPT even if apertures are being applied.