Suffering embarrassment when skilfully taking a cast off (9)

I believe the answer is:

abashedly

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'suffering embarrassment when' is the definition.
I can't judge whether this defines the answer.

'skilfully taking a cast off' is the wordplay.
'skilfully' becomes 'ably'.
'taking' means one lot of letters goes inside another.
'cast off' becomes 'she'd' (shedding is a kind of casting off).
'a'+'shed'='ashed'
'ably' placed around 'ashed' is 'ABASHEDLY'.

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I've seen this clue in The Guardian.

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