Aardwolfe--

Are you sure you're looking at a toothpick? Your description (“The toothpick is a metal rod, about 3/32" in diameter and a bit over 2" long.") sounds more like the pen from my SwissChamp, which is basically half of a standard refill with a grey tip, as on the tweezers, and fits in a recess under the scale, as does the toothpick & tweezers. The 'picks on ALL my SAKs that have them (mostly Victorinox, but there's a couple of Wengers that were given to me) are flat, tapered to a point, ivory colored, and plastic.

I’ve used them, infrequently, but with great success—most memorably, to remove a fish bone wedged tightly between two teeth while dining at a fancy restaurant. That bordered on painful, but the Classic saved the day (much preferable to the 4” Puma Game Warder I carried at the time:) )

David