In search and rescue (SAR) operations, drones can provide clear and timely situational overview data and object identification. However, the current one-to-one relationship between operators and drones limits scalability. Swarm solutions have been proposed to overcome this limitation, but there are few examples of control concepts for SAR operations. Human-swarm interaction (HSI) presents new challenges in terms of task design, control loops, communication, and managing uncertainty. We present an exploratory study of integrating drone swarms into SAR organizations, with a focus on challenges and opportunities for HSI. Our findings highlight the need for a holistic approach to drone swarm systems design, development, and integration. Careful system and task design is vital to reduce operator workload, maximize situational awareness, and maintaining effective communication among SAR team members. Building trust through technology exposure and training is also important. We identify several key research avenues, including adaptive and intelligent swarm control mechanisms, trust dynamics between operators and swarms, participatory design work, legal and operational frameworks, and the organizational impact of drone swarm integration. Overall, this paper contributes to HSI and SAR research by addressing research gaps concerning the integration effects and constraints of drone swarms in current work settings. The study highlights the potential for implementing drone swarms in semi-voluntary SAR organizations, while emphasizing the importance of considering the tasks and interactions between humans and drones when assessing overall system performance.