Most people on board a ship have multiple duties. Cook/Seaman should certainly count as sea service. It will be up to your Captain whether he is willing to sign your "Letters of Sea-Service." These letters specify what vessels you worked on - including their registration numbers, length, tonnage, and type of propulsion - between what dates, performing what duties, and in what waters. The letters must be originals, preferably on a company letterhead, and be signed by the licensed captain or a company officer from the named vessels.
You will need 360 days of sea time with 60 of those days within the last year.