The fewest switches surface hopping method has been widely used for the simulation of charge transport in organic semiconductors. In the present study, we perform nonadiabatic molecular dynamics (NAMD) simulations of hole transport in anthracene and pentacene. The simulations employ neural network (NN) based Hamiltonians in two different nuclear relaxation schemes, which utilize either a precalculated reorganization energy or site energy gradients additionally obtained from NN models. The performance of the NN models is evaluated in reproducing hole mobilities and inverse participation ratios in terms of both quality and computational cost. The results show that charge mobilities and inverse participation ratios obtained by models, which were trained on DFTB or DFT training data, are in very good agreement with the respective QM reference method for implicit relaxation and, where available, also for explicit relaxation. Reasonable agreement with experimental hole mobilities is achieved. Utilizing our models in NAMD simulations of charge transfer amounts to a reduction of the computational cost in a range of 1 to 7 orders of magnitude compared to DFTB and DFT. This proves neural networks as promising tools for the improvement of accuracy and efficiency of charge and potentially also exciton transport simulations in complex and large molecular systems.