Artillery Men for the most part did not use sidearms as their job was to man the gun, not shoot at individuals. However, many often equipped themselves with various revolvers of a variety of makes. So with revolvers, as long as it is period correct, you would likely be okay. I would go for a dragoon or later model Colts over a Walker as they are more likely to have been carried than a Walker. (I have not to date actually seen documentation where a Walker was used in the CW, where there is large documentation on the later models. I am confident it happened, just haven't read any credible source that the Walker was carried/issued.)
Long arms are a little different. Many Confederate artillery units carried a few musketoons, muzzle loaded carbines with barrels of 24-26". They differed from the Calvary version in that they had standard sling rather than a calvary slide bar/ring type sling. Enfields were fairly common. Cook and Brother, Dickson and Nelson, Richmond, and J. P. Murray were the more common makers of Confederate Artilery Musketoons.
In addition, there was an "Foot Artillery Sword" that I am not sure if it is part of the gun crews equipment or carried by individuals. It resembles a Gladiator/Roman Infantry type of sword. It had a short heavy thick double edge blade 18"-24" long with a heavy brass hilt. I believe it was more likely standard equipment to cut a dead horse out of their traces so the piece could continue on with the surviving horses. It might however make a very formidable weapon in close combat.
I don't think the LeMat would do as that was mainly a Calvary/navy weapon. While a unique weapon with Southern association, only about 1500 made it into the country. Many(about half if I remember right) of those were rejected by Southern inspectors as unfit for service.