If I happened to be Usopp, and I recognized that I had received my Father’s fabulous skills with the projectile, I would simply have gone to the neighbourhood Gun store and got out the genuine Gun in there.
Usopp apparently didn’t know he had any special talent. He was simply a Child playing nearby with a toy, and he felt that he was particularly good with it. It’s not something that got him go believe “my god, I would be a goner with an actual weapon, I should get one”. He lived in a nonviolent village.
Even if he desired a Gun, who in their sane mind would trade one to the slightly-crazy child who resides solely at the end of the village. I mean, a gun-store completely would, those people don’t care who they’re marketing to, just Gun-stores aren’t typically located in small villages in the centre of nowhere.
The first chance Usopp had to get a Gun was in Loguetown. At this time, he’d already struggled with the Slingshot a slew of events, he knew how to handle it in a fight, unlike Guns. Usopp was shocked when he crashed something with the canon on Going Merry. Why would he deem, he could handle a Gun? He apparently could, but a bit of Usopp’s personality is that he doesn’t hold a lot of faith in himself.
As for why he’s, however, using a Slingshot presently, well, soon it has been shown to be an excellent weapon, so why should he switch it to something he’s not trained to?
Also, I crave to name out that throughout his two-year training, he was thrown to forest island without a Gun shop.
Usopp’s use of a Slingshot is intended to tell us that he’s not a fighter. He wasn’t prepared. He was only a Child nobody bothered about, a kid nobody believed had any skill. Nobody provided him with a weapon, he built it himself out of stocks and a part of rubber.