During the COVID-19 pandemic, uncertainty has increased in many areas of both business supply and demand, notably oil demand and pricing have become even more unpredictable than before. Thus, for companies that buy large quantities of oil, effective oil price risk management is crucial for business success. Nevertheless, businesses’ risk appetite, specifically willingness to accept more risk to achieve desired business benefits, varies significantly. The aim of this paper is to deepen the analysis of the effectiveness of employing artificial neural networks (ANNs) in hedging against oil price changes by searching for buy signals for European WTI (West Texas Intermediate) crude oil call options, while taking into account the level of risk appetite. The number of generated buy signals decreases with increasing risk appetite, and thus the amount of capital necessary to buy options decreases. However, the results show that fewer buy signals do not necessarily translate into lower returns generated by networks in a given class. Thus, higher levels of return on the purchase of call options may be obtained. The conducted analyses clearly proved that ANNs can be a useful tool in the process of managing WTI crude oil price change risk. Using the analyzed network parameters, up to 29.9% of the theoretical maximum possible profit from buying options every day was obtained in the test set. Furthermore, all proposed networks generated some profit for the test set. The values of all indicators used in the analyses confirm that the ANNs can be effective regardless of the level of risk appetite, so in this respect they may be described as a universal decision support tool.