I was on two WW-II boats in the late 1950s...in our gun locker we had one BAR, a couple of Thompsons, a couple of M-1s, and 4 or 5 1911A-1s. Never saw anybody carry when we were underway - anything hanging off your belt would get hung up on any number of pipes, valves, knobs, switches, etc. Not a good thing. As said above, the topside watch carried a 1911, empty magazine in the piece, two full mags in an ammo pouch on the guard belt.
Also, I've read medical reports from all of our WW-II war patrols, there were indeed cases of combat fatigue - both officers and enlisted - but the captain never had to use a firearm to control the poor guy who broke down.
If anybody is interested in a link to these medical reports, PM me and I'll send it along.
Now during WW-II, many times our boats searched/destroyed Japanese fishing boats...the boats had radios which would be used to report our positions and American airplane raids. Everybody was armed while doing this with small arms, plus, of course, the deck guns were manned and ready. Lots of WW-II film of these events. I've been told that if the fishing boat had a 2-way radio, it was burned/sunk. If is was just a simple fishing boat, it was left to go on its way.