Noise-reducing gizmo Sikh fixed in shed (4,3)

I believe the answer is:

hush kit

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'noise-reducing gizmo' is the definition.
I know nothing about this answer so I can't tell whether this works.

'sikh fixed in shed' is the wordplay.
'fixed' is an anagram indicator.
'in' indicates putting letters inside.
'shed' becomes 'hut' (I've seen this before).
'sikh' anagrammed gives 'shki'.
'shki' put into 'hut' is 'HUSH KIT'.

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I've seen this clue in The Times.

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