This research studies the influence of the addition of defatted press cakes (from the production of hazelnut, camelina, pumpkin, and hemp seed oil) on nutritionally important components: fibre, resistant starch, polyphenols, hydroxymethylfurfural (HMF), and acrylamide in directly and indirectly expanded snacks. The amounts of press cakes added to corn grits were 3, 6, and 9%. Extrusion was carried out in a laboratory single-screw extruder. For indirectly expanded products (SCFX), supercritical CO2 was injected during extrusion, and secondary expansion was completed in the microwave oven. The type and content of press cake, as well as the type of product, significantly influenced total polyphenol content and antioxidant activity. Press cakes increased the contents of both soluble and insoluble fibre (from 1.94% d. m. and 1.28% d. m. for extrudates without press cakes up to 3.17% d. m. and 6.94% d. m. for SCFX extrudates with press cakes, respectively), and resistant starch was not markedly influenced by their addition. The influence of the content of press cake on HMF was not significant, whereas the type of cake and the type of extrusion influenced HMF significantly. In a raw mixture of corn grits with 3% of pumpkin press cake, HMF was below the limit of detection, and the highest content was found in the classically extruded sample with the addition of 9% of camelina press cake (580 ppb). In all samples, the acrylamide content was below the limit of detection, indicating that safe products were obtained. This research shows potential for the implementation of supercritical CO2 extrusion in the production of safe, nutritionally improved snack products. Future research might bring about the design of cost-effective processes applicable in the industry.