You don't really need squid ink.
Any kind of ink would work.
Have you seen any ink?
With any quills in it?
Where do people normally keep their writing utensils?
On their desks.
On the desk in the captain's quarters is some ink with a quill in it.
Take the ink. (You'll also have to take the quill to be able to take the ink.)
Now add the ink to your Monkey Island Mix.