Replacing a verb with 'does, did, etc'

The man uses the sharp end of the stick in his hand, as he uses the steel end of his boot on his foot.

I understand that 'do, does, done, and did' can replace the verb (predicate).

For some reason, in this setence, I want to insert with, even though I'm pretty sure it shouldn't be. Can you tell me which is the correct version please?

a) The man uses the sharp end of the stick in his hand, as he does the steel end of his boot.

b) The man uses the sharp end of the stick in his hand, as he does with the steel end of his boot.

Thanks