Green extraction was applied to Argentinean shortfin squid (Illex argentinus) viscera, consisting of a wet pressing method including a drying step, mechanic pressing, centrifugation of the resulting slurry, and oil collection. To maximise the oil yield and ω3 fatty acid content and to minimise the oil damage degree, a response surface methodology (RSM) design was developed focused on the drying temperature (45–85 °C) and time (30–90 min). In general, an increase of the drying time and temperature provided an increase in the lipid yield recovery from the viscera. The strongest drying conditions showed a higher recovery than 50% when compared with the traditional chemical method. The docosahexaenoic and eicosapentaenoic acid contents in the extracted oil revealed scarce dependence on drying conditions, showing valuable ranges (149.2–166.5 and 88.7–102.4 g·kg−1 oil, respectively). Furthermore, the values of free fatty acids, peroxides, conjugated dienes, and ω3/ω6 ratio did not show extensive differences by comparing oils obtained from the different drying conditions. Contrary, a polyene index (PI) decrease was detected with increasing drying time and temperature. The RSM analysis indicated that optimised drying time (41.3 min) and temperature (85 °C) conditions would lead to 74.73 g·kg−1 (oil yield), 1.87 (PI), and 6.72 (peroxide value) scores, with a 0.67 desirability value.