Fur, I hesitate to say, belonging to me (6)
I believe the answer is:
ermine
'fur' is the definition.
(I know that ermine is a type of fur)
'i hesitate to say belonging to me' is the wordplay.
'i hesitate to say' becomes 'er' (expression used when hesitating).
'belonging to me' becomes 'mine' (I've seen this in another clue).
'er'+'mine'='ERMINE'
(Other definitions for ermine that I've seen before include "White fur worn by some judges" , "Ceremonial fur" , "Stoat's winter fur" , "White fur of stoat" , "White fur of weasel" .)