Context. The winds from a non-accreting pulsar and a massive star in a binary system collide forming a bow-shaped shock structure. The Coriolis force induced by orbital motion deflects the shocked flows, strongly affecting their dynamics. Aims. We study the evolution of the shocked stellar and pulsar winds on scales in which the orbital motion is important. Potential sites of non-thermal activity are investigated. Methods. Relativistic hydrodynamical simulations in two dimensions, performed with the code PLUTO and using the adaptive mesh refinement technique, are used to model interacting stellar and pulsar winds on scales ~80 times the distance between the stars. The hydrodynamical results suggest the suitable locations of...