Computational electromagnetics studies the phenomena of electromagnetic wave propagation, which is governed by Maxwell's equations - four coupled Partial Differential Equations (PDEs) that must be solved numerically in realistic settings. One of the simplest and most widespread methods for that is the Finite Difference Time Domain (FDTD) method, which discretises the domain into a staggered grid (also known as Yee grid) and applies the central finite differences to discretise the PDE, resulting in an efficient explicit scheme. The goal of our work is to generalise the FDTD to a meshless setting. Besides the clear reason of greater geometric flexibility of meshless methods, an important motivation for our work is the known dispersion anisotropy of the FDTD, which we expected to vanish in the meshless approach, as there is no grid present that would introduce anisotropy of the method. In order to do so, we employ the Radial Basis Function-generated Finite Differences (RBF-FD) with Polyharmonic Splines (PHS) and monomial augmentation. To generalise the FDTD we have two natural approaches: The first is to directly apply RBF-FD, discretising the differential operators appearing in Maxwell's equations in the usual manner. The second is to use the "virtual stencil approach" and interpolate the unknowns to a virtual Yee stencil, on which we can then locally apply FDTD. Both approaches turn out to be consistent with a major trade-off - the timestepping is unstable. We then turn to stabilising the methods by adding a Hyperviscosity (HV) term to the system and discuss the suitable HV parameters for our problem. We demonstrate that both of our HV-stabilised methods can sucessfuly solve the Maxwell's equations with negligible error. Finally, we turn to the analysis of dispersion, where we demonstrate that we can vary the magnitude of the dispersion by changing the stencil size in the RBF-FD approach. Additionally, we show that such an approach results in a method with an isotropic dispersion relation.