Paddle when content to swim (5)

I believe the answer is:

bathe

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'swim' is the definition.
(bathe can mean to swim)

'paddle when content' is the wordplay.
'paddle' becomes 'bat' (I can't justify this - if you can you should give a lot more credence to this answer).
'content' indicates the central letters.
The centre of 'when' is 'he'.
'bat'+'he'='BATHE'

'to' acts as a link.

Can you help me to learn more?

(Other definitions for bathe that I've seen before include "Take dip in sea" , "bit of swimming" , "Swim or paddle" , "Wash, soak" , "Suffuse" .)

I've seen this clue in The Daily Express.

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