After the detection by the H.E.S.S. Cherenkov telescope of the very-high-energy 𝛾 rays coming from the colliding wind binary 𝜂 Carinae, we explored the possibility that its spectral cut-off is not due to an intrinsic cut-off in the accelerated particle population, but rather being a feature arising from the 𝛾-𝛾 opacity. We developed a model which reproduces the expected 𝛾-𝛾 absorption between the very-high-energy 𝛾 rays interacting with the intense ultraviolet fields of both stars, assuming the two most likely orbital orientations. Thanks to its deep sensitivity, the Cherenkov Telescope Array (CTA) has the potential to exclude one of the two orientations detecting fast spectral variability on daily/weekly timescale, when at periastron the orbital positions of the two stars vary the most. It can also constrain the magnetic field and the spatial locations where particles are accelerated to their highest energy via diffusive shock acceleration. The eventual detection by CTA of a rising spectrum due to the Rayleigh-Taylor tail of the absorption will be the indisputable confirmation that colliding wind binaries can accelerate particles to energies larger than those one found in supernova remnants.