This study seeks to assist small and medium enterprises break free of the constraints of the conventional financing model and lessen the supply chain finance risks they face. First, the supply chain financial business model and credit risk are analyzed, followed by a discussion of the application principle of blockchain in the control of supply chain financial credit risk. The next topic up for discussion is the emancipation of individuals and the application of financial technology toward the management of financial risk in supply chains. In the final stage of the development of the computerized risk assessment model, the Fuzzy Support Vector Machine (FSVM) is optimized, and the effectiveness and efficiency of risk classification are enhanced by introducing a variable penalty factor C. To test the efficacy of the C-FSVM risk assessment model, the Chinese auto sector is used as the study’s object. According to the results of the study, the C-FSVM model has a classification accuracy of 96.35% for the entire sample, 96.45% for credible firms, and 95.34% for default enterprises. The training time of the C-FSVM model is 473.9s, which is far lower than the SVM and FSVM models’ training times of 1631.6s and 1870.2s. In summary, the C-FSVM supply chain financial risk assessment model is effective and has great application value in banking practice.