I want to start listing a set of assumptions that have to be made:
- Ships of the time weren't meant for long trips, and weren't able to sail into the deep seas. Ships would follow the coasts and stop at night, at a port if possible.
- The most common ship of the time was the Galley: it was oar powered and usually had between 10 to 15 pairs of rows of oars. It also could be supplemented with square sails. If you want to strech a bit your history, the Bedens are a bit more modern (but still pre age of sail), equipped with lateen rigs and required less sailors to operate, although they were definitely smaller than Galleys.
- Fresh Vegetables and fruits were a thing for rich people and farmers.
- The main crops in the horn where, in order, Barley, Wheat and Teff. Of these three, only Teff is indigenous to the horn. The others can be found anywhere.
- Salting was the most common preserve, and was used for meat, fish and vegetables.
With these assumptions, I think a sailing merchant ship of the time would always carry:
- Barley: it was easy to store, could be made into porridge without milling it, and also was used to keep the water from spoiling by making weak ale from the bread or the grains.
- Salted goods: Sailors usually ate more proteins than farmers. A bit of salted protein would be added to the porridge for flavour, protein and salt. Pickled vegetables could also be added to the porridge for flavouring.
Note I mention a lot the word porridge: That's because is going to be the staple food of your sailors. These ships seldom had a dedicated cook (they crews weren't that big) so one of the sailors would just put a cauldron with water, grains and meat to heat; a simple dish but effective.
Optionally, you could also load a bit of cheese, barley bread and of course, supplement the meals with freshly caught fish. If they are sailing from one of their home ports, they will probably will also carry some teff bread, or teff grains (yes, you guessed right, for the porridge).
In the end, the most important thing to remember is that ships of that period tend to sleep at ports. That means cheap or underpaid sailors will eat porridge. The others will probably eat at taverns where, while the ingredients will be largely the same, they will be at least prepared by someone who -hopefully- can cook, and they won't be as salty.
I won't consider this as "food" but khat consumption has been and still is very common in the horn. It's a plant that acts like a stimulant when chewed on (like coca leaves). Khat ideally has to be consumed fresh but I won't be the patron who denies khat to his sailors (not if I don't want an early water grave).
As for the patron of the ship, I would carry a small quantity of flour (of any of the cereals) to make unleavened bread (think a taco tortilla) called Qitta, as well as perhaps fresh vegetables that would last until the next port for making a meat and vegetable stew (there are many recipes, but in the end consist of putting everything on a pot and cooking it). Of course he can afford to have nice foods because he will probably have an attendant for doing these kind of chores (and no, the attendant will not cook for the sailors, there are classes, you know).