Hyperviscosity has recently emerged as a promising stabilisation method for hyperbolic partial differential equations. The method introduces a high-order Laplacian term to dampen the spurious modes that would otherwise lead to divergence of the solution. The use of a higher-order operator reduces the numerical degradation of the solution compared to a simple artificial viscosity scheme, but poses a more difficult computational problem. To reduce the numerical complexity and the effect of the unbalanced boundary stencils, we can use different approximation approaches for the core equation and the stabilisation term. In this presentation, we will investigate how various RBF- based approximation methods for the hyperviscosity operator and their parameterizations affect stability and accuracy. We will also investigate to what extent the recommended parameterization can be stretched without compromising the stabilisation properties.