The need for low-carbon development has become a social consensus. Increasing numbers of enterprises implement carbon emission reduction by using carbon cap-and-trade mechanisms to cater to consumers and practice social responsibility. From the manufacturer’s perspective, they can implement carbon emission reduction investment by themselves or outsource it to the retailer or energy service company (referred as ESCO). To explore the best carbon emission reduction mode selection strategy, we built and compared three carbon emission reduction modes—manufacturer emission reduction, retailer emission reduction, and ESCO emission reduction—by using Stackelberg game models. The joint decisions of operation, finance, and environment were obtained by using the backward induction approach. The impacts of key parameters were analyzed, such as the retailer’s initial capital amount and the decision-makers’ risk aversion degree on the low carbon supply chain operation. Our results show that the optimal carbon emission reduction mode for the manufacturer is changed as the retailer’s initial capital amount changes. Carbon emission reduction by the ESCO (retailer) becomes the dominant strategy for both the economy and environment when the cost advantage (cash investment ratio) of the ESCO (retailer) carbon emission reduction mode is sufficiently high (low). Overall, decision-makers’ risk aversion is detrimental to both the economic and environmental developments of the supply chain. We also designed contracts to realize the coordination of risk-neutral, risk-averse, capital-adequate, and capital-constrained low-carbon supply chains. These results give guidance for decision-makers to better manage the low-carbon supply chain in the context of fully considering the influential factors of risk aversion and capital constraint.