Don't confuse the
Scottish dirk with a Naval dirk. The blades do not have much, if anything, in common other than the fact they are straight.
Naval dirks are almost always quillon daggers with a narrow, straight stilleto blade. As mentioned before, they were carried exclusively by Midshipment who could be boys 8-20 years of age. Midshipment were "cadets" who were learning the naval officer trade the hard way. Technically, as "non-officers" or at most warrant officers, they had command but were not commissioned. As such, they were not entitled to a sword which was an emblem of rank along with the epaulette. The dirk was a compromise. If there was real fighting to be done, I am sure they grabbed one out of the weapons slop chest just like any sailor. Midshipmen after learning their trade had to stand for a written and practical oral exam on seamanship to achieve the first commissioned rank of Lieutenant. The C.S. Forrester "Hornblower" books give a very nice account of this process - although fictional it is based on the life of a real naval officer who through attrition died as Admiral of the Fleet.
The Scottish Dirk is a complicated beast. It was made from broken sword blades (both broad and back swords) and blades forged for the task. The grip could be plain, elaborately carved, or made of pewter or brass. They were usually 12-16" ong and mostly single-edged when made for purpose. My opinion is that the common man carried a similar blade on a much more utilitarian, plain grip weapon and the dirk as we know it today survived because it was costly, carved, and the tool of a man better off than most.
A sailor would have probably had a penny knife that looked very much like a modern rivited butcher knife in a plain leather sheath. I have recently heard somewhere - and I forget the source - that even today's anti-terrorism special forces just tend to use well-tempered commercial kitchen knives with a good grip wrapped in duct tape for better handling rather than the high-priced, speciality blades that abound. Okay, I'll come clean. I have a friend that does this sort of sneak-in-the-dark stuff at Ft. Bragg (get it, Ft. Bragg?) I'll bet these sailors did the same. Cheap knives and well used.
Good luck and welcome to the Forum.
Good luck!