Unwilling to be sick (10)
I believe the answer is:
indisposed
I believe this clue is a double definition.
'unwilling' is the first definition.
(thesaurus)
'sick' is the second definition.
('indisposed' can be similar in meaning to 'sick')
'to be' is the link.
(Other definitions for indisposed that I've seen before include "Out of sorts" , "Slightly unwell" , "Poorly" .)