Idiot to have wife exchange (4)

I believe the answer is:

swap

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'exchange' is the definition.
(I know that swap is a type of exchange)

'idiot to have wife' is the wordplay.
'idiot' becomes 'sap' (I can't justify this - if you can you should believe this answer much more).
'to have' means one lot of letters goes inside another.
'wife' becomes 'w' (abbreviation).
'sap' placed around 'w' is 'SWAP'.

Can you help me to learn more?

(Other definitions for swap that I've seen before include "Switch" , "trade" , "Change over" , "Exchange goods" , "Wasp (anag)" .)

I've seen this clue in The Daily Express.

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