Reluctant to admit Swann's content playing far less effective spinner (6)

I believe the answer is:

conway

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'far less effective spinner' is the definition.
The definition suggests a singular noun which matches the answer.

'reluctant to admit swann's content playing' is the wordplay.
'reluctant' becomes 'coy' (I am not sure about this - if you are sure you should believe this answer much more).
'to admit' indicates putting letters inside.
'content' means to look at the middle letters.
'playing' indicates an anagram.
The middle of 'swann' is 'wan'.
'wan' with letters rearranged gives 'nwa'.
'coy' going around 'nwa' is 'CONWAY'.

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I've seen this clue in The Independent.

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