We explore the ability of high-energy observations to constrain orbital parameters of long-period massive binary systems by means of an inverse Compton (IC) model acting in colliding wind environments. This is particularly relevant for (very) long-period binaries where orbital parameters are often poorly known from conventional methods, as is the case, e.g. for the Wolf-Rayet (W-R) star binary system WR 147, where INTEGRAL and MAGIC upper limits on the high-energy emission have recently been presented. We conduct a parameter study of the set of free quantities describing the yet vaguely constrained geometry and respective effects on the nonthermal high-energy radiation from WR 147. The results are confronted with the recently obtained high-energy observations and with sensitivities of contemporaneous high-energy instruments like Fermi-LAT. For binaries with sufficient long periods, like WR 147, g-ray attenuation is unlikely to cause any distinctive features in the high-energy spectrum. This leaves the anisotropic IC scattering as the only process that reacts sensitively on the line-of-sight angle with respect to the orbital plane, and therefore allows the deduction of system parameters even from observations not covering a substantial part of the orbit. Provided that particle acceleration acts sufficiently effectively to allow the production of GeV photons through IC scattering, our analysis indicates a preference for WR 147 to possess a large inclination angle. Otherwise, for low inclination angles, electron acceleration is constrained to be less efficient as anticipated here.