Back in a storage area of the shop I have a little overhead task light, a magnifying visor, and a set or two of good jeweler's tweezers. I found that the cheap look-alike tweezers bend easily early on. When I get a sliver, I walk back to the area, switch on the light, pick up the tweezers, don the magnifying visor, extract the sliver, and go back to work.
Been doing it for 30 years.
New visors are available with LED lights. Don't know about them. The ones I use were from Northern. They were about $10.00 before they discontinued them. Had flip up lenses for various powers. As quality optics go, they are pretty awful, but good enough for short term use.