This work concerns the simulation of shear wave propagation in the cornea with a finite element model. The underlying application is the detection, through elastography techniques, of pathologies that are characterized by changes in the mechanical properties of the tissues. The cornea, as most of biological tissues, is highly hydrated, which is generally associated to nearly incompressible behavior. The finite element approximation of nearly incompressible solids is a well-known problem in literature as it interests many industrial materials and it is associated to locking phenomena: numerical stiffening, ill-conditioning of the stiffness matrix, spurious pressure. At the same time, due to large dimension, elastodynamic problems require explicit time-discretization, such as Leap-Frog method, stable under the CFL condition. The enforcement of incompressibility strongly reduces the admissible time-step, dramatically increasing the computational cost. To our knowledge, only few recent works have tried to tackle this latter problem. Here, we propose a two-fold strategy. The space discretization is focused on decreasing the computational cost for the volumetric component. We use high-order spectral elements with Gauss-Lobatto quadrature rules in order to apply mass lumping. We consider an inf-sup stable mixed formulation with Q_4 - Q_2^{disc} elements for the approximation of the displacement and the pressure field respectively. Finally, we propose a new definition of the divergence operator to efficiently compute the volumetric contribution. For the time-discretization, we consider a modified equation approach based on the use of Chebyshev polynomials, inspired by local-time stepping methods. This approach results in a relaxation of the stability condition but requires an iterative application of the volumetric operator. We obtain an energy-preserving second-order accurate scheme with a reduced computational time of a factor 3. The scheme is applied to linearized hyperelastic solids undergoing static large loads, as the cornea.