Planetesimals embedded in a protoplanetary disc are stirred by gravitational torques exerted by density fluctuations in the surrounding turbulence. In particular, planetesimals in a disc supporting fully developed magnetorotational turbulence are readily excited to velocity dispersions above the threshold for catastrophic disruption, halting planet formation. We aim to examine the stirring of planetesimals lying instead in a magnetically decoupled mid-plane dead zone, stirred only by spiral density waves propagating out of the disc’s magnetically coupled turbulent surface layers. We extend previous studies to include a wider range of disc models, and explore the effects of varying the disc column density and external magnetic field strength. We measure the stochastic torques on swarms of test particles in three-dimensional resistive-magnetohydrodynamics stratified shearing-box calculations with ionization by stellar X-rays, cosmic rays, and recombination on dust grains. The strength of the stirring is found to be independent of the gas surface density, which is contrary to the increase with disc mass expected from a simple linear wave picture. The discrepancy arises from the shearing out of density waves as they propagate into the dead zone, resulting in density structures near the mid-plane that exert weaker stochastic torques on average. We provide a simple analytic fit to our numerically obtained torque amplitudes that accounts for this effect. The stirring, on the other hand, depends sensitively on the net vertical magnetic flux, up to a saturation level above which magnetic forces dominate in the turbulent layers. For the majority of our models, the equilibrium planetesimal velocity dispersions lie between the thresholds for disrupting strong and weak aggregates, suggesting that collision outcomes will depend on material properties. However, discs with relatively weak magnetic fields yield reduced stirring, and their dead zones provide safe havens even for the weakest planetesimals against collisional destruction.