Stroke cobbler's skin with his tool (5)

I believe the answer is:

crawl

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'stroke' is the definition.
(I know that crawl is a type of swimming stroke)

'cobbler's skin with his tool' is the wordplay.
'skin' suggests removing the centre (only the skin or outside of the word is used).
'with' says to put letters next to each other.
'his tool' becomes 'awl' (I can't justify this - if you can you should give a lot more credence to this answer).
'cobbler' with its middle removed is 'cr'.
'cr'+'awl'='CRAWL'

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(Other definitions for crawl that I've seen before include "progress slowly" , "but very slowly on land" , "swarm" , "Progress, slow on land but fast in water" , "Be obsequious; swimming stroke" .)

I've seen this clue in the Sydney Morning Herald.

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