When we had pins on the production floor, we did put them in labeled handles.
When pins were used in the lab, they were plucked from the set kept at the lab work station and replaced in the same case. They were not allowed to "wander" onto the work floor - work pieces were brought to the lab if no "workshop" pins were available.
As an alternate, you might create individual labeled cases to hold pins not set in handles (access requirements come to mind for not using a handle), with training to emphasize pins be returned to case after use.
It is important to keep one set of pins as a "master" under controlled conditions.