Despite prior discussion, and concession to those that seemed to be knowledgeable on the topic, apparently some light artillerymen, privates, were quite familiar with, and had use of, personal weapons while on campaign (if not specifically issued to them). Anyway, far from "looking silly" if it really happened, eh?
These being merely casual references from one regimental history of a light artillery unit from my state: Behind The Guns - History of Battery I, 2nd Regiment Illinois Light Artillery - 1965, from original transcript by Thaddeus C.S. Brown with Samuel J. Murphy and William G. Putney (Putney was bugler for the unit):
“Captain Barnett mounted about fifty men belonging to the battery on the horses of the battery, and armed them with sabres and revolvers. The detachment had quite the appearance of cavalry as they marched out of camp...”
“When near Huntsville, Ala., Sergeant Murphy, in command of some scouts, saw two horsemen come out of the brush in front of them, and gave chase after them. They gained rapidly, and one of the rebels surrendered, but the other one being better mounted, escaped. The prisoner who was about six feet, for inches in height, after looking at his captors, said, ‘Well, I’ll be d - - d, if I hav’nt been captured by a lot of d - - d artillery men!’ He said that the Yankee cavalry had been after him, nearly two years, but could not catch him...”
“One morning Sergeant Ed. Smith started out before dawn at the head of a foraging party to collect supplies for the battery. He had a guard of about fifteen men armed with carbines, detailed for the purpose...”
There are more references to personal weapons and the enlisted men in the book, but etc. etc. - - just to point out these weren't exceptional instances to the writers, the soldiers, in that unit at the time, never the main point of the accounts.
So where did all those pistols, sabres, carbines come from...? I believe the battery wagon (battery box), which is where we should find such today in reenactment, not with front-line cannoneers servicing the primary weapon, the cannon, during a battle scenario.