Head-on collision of laser-induced plasma wakefields with differing profiles of electrostatic potential has been recently found to be an efficient mechanism for generating high-power electromagnetic emission at the second harmonic of the plasma frequency (Timofeev et al 2017 Phys. Plasmas 24 103106). This mechanism is attractive for creating a source of tunable narrow-band coherent radiation in the terahertz frequency range. In this paper, we generalize the theory of electromagnetic emission produced by non-linear interaction of two plasma wakes to the case of an arbitrary collision angle. Such a theory is used to evaluate the angular distribution of the second harmonic radiation as well as its total generation efficiency for parameters of the proof-of-principle experiment in which laser axes will be aligned with a small finite angle. Theoretical predictions are qualitatively confirmed by particle-in-cell simulations.