Yes we were sometimes issued sidearms. Once in port I was petty Officer of the watch and went into our messroom and found the man on watch lying on a bench...drunk! I took his sidearm and
I woke him as much as possible and ordered him to his quarters. I reported him to our Armed Guard commander and replaced him with another man.
Also, I had to go ashore with our AG commander in the Phillipines and wore my sidearm.
Another time, in Livorno, Italy all of us who were Petty Officers were issued sidearms because there were reports that German troops in American uniforms were in the area similar to those during the Battle of the Bulge. This happened at the same time that battle was taking place. (It was a long way off)!
There were probably many other stories of Armed Guard sailors using sidearms...and perhaps rifles. Let's hear those stories!