Nodal noncentrosymmetric superconductors can host zero-energy flat bands of Majorana surface states within the projection of the nodal lines onto the surface Brillouin zone. Thus, these systems can have stationary, localized Majorana wave packets on certain surfaces, which may be a promising platform for quantum computation. Such applications require protocols to manipulate the wave packets in order to move them without destroying their localization or coherence. As a step in this direction, we explore the idea that the surface states have a nontrivial spin polarization, which can couple for example to the magnetization of a ferromagnetic insulator in contact to the surface, via an exchange term in the Hamiltonian. Such a coupling can make the previously flat bands weakly dispersive. We aim to model the motion of spatially localized wave packets under the influence of an exchange field which is changed adiabatically.We calculate the time-evolved wave packet for a model system and discuss which factors influence the direction of motion and the broadening of the wave packet.