Anyway, the baseball caps were never issued and not really part of the official uniform as others have mentioned. Caps were optional and purchased in the ships store. I don't remember if we could purchase a ship cap at the Miramar base store or not. Mostly they just had squadron caps. While on base at Miramar we could wear our squadron cap. About the only time I can remember doing so was when I was not working. When working I either had no hat or my cranial with headset since I worked on radios.
On the ship we could wear our squadron cap, but most airwing people had no hat or the cranials. Once the ship pulled away from the pier the uniform requirements changed drastically. Off came the dungaree shirts and down to t-shirts for many depending on your work environment. For much of the airwing, enlisted stowed the dungaree shirts in their lockers and had either white, green, or an OD color t-shirt. many of us were also allowed to wear a kind of green army like work pant with our t-shirts to keep from really messing up our dungarees. Then of course there was also the colored long sleeve shirts according to our jobs for the flight deck. No hats there! It would probably get blown overboard anyway or FOD for aircraft. Cranials were strapped to your head with a chinstrap.
That's pretty much what mine was like. It also had a triangular mouthpiece/microphone that would snap on for use with the radio. Some of us found and could use a boom style mic. It was easy to tell which cranial had headsets by the black ear covers. Tan ear covers were not headsets.