When I was in the navy in the 80's, navywide policy was that it was left up to the Commanding Officer of each ship or command. Some CO's were really flexible - usually the old school, Viet Nam era guys - but some could be really strict.
I was on the Nimitz, and ships company and squadron personnel could usually carry any kind of SAK we wanted. Exceptions were made though, depending on the jobs certain people had: a lot of Bos'n Mates, supply guys, and line handler types carried the Buck 110, U.S. Schrade LB7, and similar lockbacks.
The only time I ever saw a fixed blade was when the Marines in our Marine Detachment carried them (usually a Kabar), but even then they (Kabar or any fixed blade) was very rare. Usually too much bulk, and got in the way. (Just try running to a General Quarters station through hatches, narrow doorways, narrow & crowded passageways, etc. with big equipment items hanging off of you. You'll become unpopular real quick.)
~Chris