Most of the major nursing theories are focused more on the nurse/patient relationship and on the psycho-social aspects of nursing than on the physiological and/or the performance of a technical skill. That's the root of your problem.
Assuming that you must use a nursing theory to meet the requirements of your assignment ... I recommend that you review the theories that you are comfortable with, looking for where the "safe and effective provision of phyisical care" fits into each theory. Many theories mention the need for the nurse to provide safe and effective physical care, preserve oxygenation, support normal physiological functions, etc. For example: Henderson's definition of nursing as "doing for the patient what he would do for himself is he had the skill, knowledge, etc. .." could be the key to using that theory. Maintaining physiological homeostasis during the procedure would link up with Rogers. Even Watson includes "Attending to supportive, protective, and/or corrective mental, physical, societal, and spritual envrionments" that enables the use of the theory to discuss physiological support.
Get 2 or 3 nursing textbooks and skim the theorists looking for that particular linkage. You should be able to find one that works well enough for you. Pick the one that best suits your philosophy of nursing in general -- and also has some sort of statement saying that the role of the nurse is to provide safe and effective physical care, preserve circulation and oxygenation, etc.
Look at the Synergy Model. I don't have the details in front of me, but as it was designed as a professional practice model for ICU nursing, it should accommodate a physiological/technical focus fairly well.
No ... you won't find a model that deals directly with your research question. But you will find many models that incorporate the idea that the nurse should provide competent phyisical care for the well-being of the patinet. Doing research into what actually is the best way to provide physical care would then be a legitimate nursing question according to that model.