A modified electron whistler dispersion law is derived in the cold-plasma approximation for analytical treatment and simplified numerical calculations of wave propagation in a wide range of ratios ωc/ωp of electron gyro- to plasma frequencies if the wave frequency is much less than ωp. The net contribution of ions to the wave dispersion law is expressed through the value of the lower-hybrid resonance frequency ωlhr only. This approximate dispersion law is valid in a wide frequency domain, that is, from the range of ωlhr until the domain where the contribution of ions can be neglected. A comparison of geometrical-optics ray trajectories calculated by the use of modified and total cold-plasma electron whistler dispersion laws is presented for the case of the Earth's plasma environment. Computer simulations of dynamical spectra of whistler waves excited by lightning discharges and registered in remote regions of the Earth's plasmasphere reveal good numerical stability of the developed ray-tracing code.