I was about to make the joke "They get splinters very well, thank you" but then I realized what community this is, so I won't make the joke.

“Oh, good Lord, didn't anybody here build ships in bottles when they were boys?”

Possibly from handling artifacts, cargo, etc? Maybe the replicators of the era leave some rough edges (literally)?

Space pallets.

They probably a tree-species crewmember onboard.

I was going to say maybe an away mission, but now I'm wondering if the transporter wouldn't just filter it out when beaming back?

It's always Sally from hydroponics.

Yes, I imagine metal and glass splinters would happen, but we routinely get hair-splinters (something about how a sock holds it, skin flexes, and body weight). So yeah, sounds plausible to me even with so little as "wearing socks".

I forget, do the replicators produce utensils to go with the food or is there like a reusable set somewhere? If the former, maybe some dish or another comes with wooden chopsticks or such out of tradition? Or perhaps some species or another might have a diet that includes wood in some way and they can accidentally leave splinters around like crumbs or something.

When you control panels regular explode with rocks flying all over the place .... I'm pretty sure splinters can be common as well

They have hand-made objects and can replicate wood. Tho this made me wonder... If the holodeck's safety protocols are working as intended, could Sisko end up getting a splinter from his holographic wooden baseball bat? 🤔

A flake of chipped paint could become a splinter

Cable stranding is a common way to get a metal splinter, but they already established that copper cables are not used on a ship (which I find just unrealistic, you can't just wirelessly power and transmit everysingle thing on a ship).