Have posted a response on the wrong enquiry. If you look on cornwall-opc-database.org there are loads of Cock names, David baptised 26.12.1797 son of Thomas and Mary Nee Best. Married 1793.
re the battle of Trafalgar, found a William Martin on the Bellerophen 14.11.1804 aged 38 from Plymouth. so could be Marys father, he could have joined up after she was born.
Family legends do sometimes have a glimmer of truth, its just finding the right information. Given she had 2 husbands there was always the possiblilty that the information came on from a different line.
Hope this has not been too confusing!!