Conventional epidemiological studies of infections spreading through trade networks, e.g. via livestock movements, generally show that central large-size holdings (hubs) should be preferentially surveyed and controlled in order to reduce epidemic spread. However, epidemiological strategies alone may not be economically optimal when costs of control are factored in together with risks of market disruption from targeting core holdings in a supply chain. Using extensive data on animal movements in supply chains for cattle and swine in France, we introduce a method to identify effective strategies for preventing outbreaks with limited budgets while minimizing the risk of market disruptions. Our method involves the categorization of holdings based on position along the supply chain and degree of market share. Our analyses suggest that trade has a higher risk of propagating epidemics through cattle networks, which are dominated by exchanges involving wholesalers, than for swine. We assess the effectiveness of contrasting interventions from the perspectives of regulators and the market, using percolation analysis. We show that preferentially targeting minor, non-central agents can outperform targeting of hubs when the costs to stakeholders and the risks of market disturbance are considered. Our study highlights the importance of assessing joint economic-epidemiological risks in networks underlying pathogen propagation and trade.