in DnD settings there isn’t exactly lore about how they get weapons. in previous editions the assumption was they use what they had in life, what is lying nearby, or whatever the necromancer who raised them hands them.

many of the design choices in 5e are to streamline new players into the gameplay without minutiae like “how many shortswords should I keep on hand to pass out to the skeletons I summon” or “can they wield exotic weapons they held in life”. but, yes a solid DM can draw on knowledge of the game to tamper with stuff like this without breaking the game. like having a death god who grants shortswords to boney boys or allowing a player to arm them with other things