A coxswain was originally a servant , or swain, whose job was to steer a
ship's boat, a cockleboat or cock (cock comes from Old French coque, which
was probably a descendant via late Latin caudica 'canoe' of Latin caudex
'treetrunk' and swain is a borrowing from Old Norse sveinn 'boy, 
servant'). 
The abbreviation cox seems to have developed in the 19th century.  -- from
Dictionary of Word Origins