HHO methods [3, 1] rely on a pair of unknowns, attached to the mesh faces and the mesh cells. They offer various assets such as the support of polyhedral meshes, local conservation principles, optimal convergence rates, and computational efficiency. HHO methods were bridged to HDG methods in [2]. [1] successfully tested the HHO methods for wave propagation in (strongly) heterogeneous media. Explicit time-marching methods are preferred in the context of fast dynamics and non- linear problems. However, when the wave equation is discretized using the second-order formulation in time, HHO methods lead to a semi-implicit problem. Indeed, the coupling between cells and faces unknowns requires the inversion of a nondiagonal matrix at each time step, which is a costly operation. We present here an explicitation algorithm based on a splitting of the HHO operators. This splitting is iterated and converges to the expected solution, if the coefficient weight- ing the stabilization is large enough. This splitting replaces the nondiagonal matrix inversion by the iterative resolution of block diagonal linear system. Experiments on the preservation of optimal convergence rates and computational costs will be reported.