With high risk of sustained transmission and substantial associated morbidity, Lumpy Skin Disease (LSD) of cattle presents a major emerging threat to bovine herds worldwide, and has the potential to cause huge losses for farmers, producers, and the wider bovine and dairy trade industries. The epidemic which started in June 2025 in France illustrates this threat, as the government-imposed mass culling strategy has led to protests by farmers and social unrest throughout the country. Here, we developed an infectious disease modelling framework for evaluating different intervention strategies in an effort to critically evaluate the evidence behind the drastic measures being taken. By simulating epidemics under different response settings, we found that control strategies employing targeted culling were essentially as effective as those requiring mass culling, and did not require significantly more vaccination. These results question the response strategy currently imposed by the French government, and suggest avenues for alternative response strategies which could gain better support from the affected communities. Our results are entirely reproducible using a new free, open-source simulation tool which can be used for further evaluation of public health interventions against LSD epidemics.