Background: Nurses face the risk of new onset occupational asthma (OA) due to exposures to cleaning and disinfection (C&D) agents used to prevent infections in healthcare facilities. The objective of this study was to measure nurses’ preferences when presented with simultaneous OA and respiratory viral infection (e.g., COVID-19) risks related to increased/decreased C&D activities. Methods: Nurses working in healthcare for ≥1 year and without physician-diagnosed asthma were recruited for an online anonymous survey, including four risk–risk tradeoff scenarios between OA and respiratory infection with subsequent recovery (Infect and Recovery) or subsequent death (Infect and Death). Nurses were presented with baseline risks at hypothetical “Hospital 1”, and were asked to choose Hospital 2 (increased OA risk to maintain infection risk), Hospital 3 (increased infection risk to maintain OA risk), or indicate that they were equally happy. Results: Over 70% of nurses were willing to increase infection risk to maintain baseline OA risk if they were confident they would recover from the infection. However, even when the risk of infection leading to death was much lower than OA, most nurses were not willing to accept a larger (but still small) risk of death to avoid doubling their OA risk. Age, work experience, and ever having contracted or knowing anyone who has contracted a respiratory viral infection at work influenced choices. Conclusions: We demonstrate the novel application of a risk–risk tradeoff framework to address an occupational health issue. However, more data are needed to test the generalizability of the risk preferences found in this specific risk–risk tradeoff context.