Fixed, one might say, with skill and sensitivity (4)
I believe the answer is:
tact
'skill and sensitivity' is the definition.
(being tactful is being sensitive)
'fixed one might say' is the wordplay.
'fixed' becomes 'tacked' (tacking is a kind of fixing).
'one might say' indicates a 'sounds like' (homophone) clue.
'tacked' sounds like 'TACT'.
'with' acts as a link.
(Other definitions for tact that I've seen before include "Sensitivity in dealing with people" , "Consideration and sensitivity" , "Diplomacy or discretion" , "Fine perception" , "Sensitivity in dealings" .)