Answer:
(C) I feel I have done my best to complete all my assigned work shifts and work emergency shifts when asked. I hope you understand my position.
Explanation:
From all the options, it can be said that (C) is the most appropriate language to be used in a letter to a superior, when being assigned a work assignment that may be deemed controversial in some way.
(A) might be suitable but choosing to use the word "defuncted", which means "no longer working or functioning" may not be an appropriate way to decline to do your assigned work, since it can be interpreted as a resignation. (B) and (D) are too informal, thus making (C) the best option since it used appropriate language and includes a reasonable explanation.