Weakly hydrated samples of platelet‐shaped nano‐particles obtained by dry‐pressing suspensions of the synthetic Na fluorohectorite clay are studied. The particles consist of stacks of several tens of 1 nm‐thick nanosilicate platelets. They form a compound of quasi‐two‐dimensional particles whose average director is aligned with the direction of the uniaxial stress applied at dehydration. Small‐angle X‐ray scattering images from these samples are either isotropic or anisotropic, depending on the sample orientation with respect to the X‐ray beam. From anisotropic images, changes in the scattering objects' orientation distribution probability (ODP) function are investigated as the temperature is lowered, thus triggering swelling of the individual particles by water intercalation. This is done, on the one hand, by inferring the width of the ODP function from the eccentricity of quasi‐elliptic iso‐intensity cuts of the small‐angle scattering images, and, on the other hand, by obtaining the ODP function from azimuthal profiles of the images. The decays of the scattering intensity as a function of momentum transfer along the two principal directions of the images exhibit power law behaviors. A crossover scale between two power law regimes is observed on the profiles recorded along the horizontal axis; it corresponds to the typical pore size along the direction of the initially applied load. These results are compared with a previous study of similar systems.