In the Figure, the profiles would thus represent the possible amplitudes of the timing residuals obtained when fitting a Schwarzschild model to the TOA data for a pulsar that orbits one of the possible alternatives to the Schwarzschild black hole considered here. A notable feature from our profiles is that for edge-on orbits case, we always find an abrupt change in the propagation time when the pulsar is at superior conjunction due to the strong curvature of photon paths to go from the emitter to the observer and to the strong impact of the Shapiro delay for such photons. Indeed, this effect is not present for inclined orbits (for which superior conjunction is never realized). Furthermore, the departure between the different profiles from the Schwarzschild propagation time exhibits a secular increment due to the increase in the orbital precession as a result of a change in the underlying space-time geometry, which leads to an increasing departure of the spatial position along the orbit from where the photon starts. Finally, all the mentioned effects, have an amplitude that depends on the value of the theory parameter and on the orbital properties of the object at hand. Such departures in the photon propagation time, expressed in seconds, can span several orders of magnitude when particularized for the SMBH at the center of the MW. Moreover, the same object orbiting different space-time geometries generates different propagation delay profiles, not only in terms of amplitude but also of functional dependence on the orbital phase, presenting peculiar features that can provide an efficient way to identify the underlying theory of gravity.