Integrating radio-sensing functionalities into future cell-free (CF) wireless networks promises efficient resource utilization and facilitates the seamless roll-out of applications such as public safety and smart infrastructure. While the beamforming design problem for the CF integrated sensing and communication (ISAC) paradigm has been addressed in the literature, existing methods rely on centralized signal processing, leading to fronthaul load and scalability issues. This paper presents a two-stage beamforming design for the CF ISAC paradigm, aiming to significantly reduce the fronthaul load by distributing the signal processing tasks between the central unit (CU) and the access points (APs). The design optimizes the sum signal-to-interference-plus-noise ratio (SINR) for communication users, subject to per-AP power constraints and signal-to-noise ratio (SNR) requirements for radio-sensing purposes. The resulting optimization problems are non-convex and challenging to solve. To address this, we employ a majorization-minimization (MM) approach, which decomposes the problem into simpler convex subproblems. The results show that the two-stage beamforming design achieves performance comparable to centralized methods while substantially reducing the fronthaul load, thus minimizing data transmission requirements over the fronthaul network. This advancement highlights the potential of the proposed method to enhance the efficiency and scalability of cell-free MIMO ISAC systems.