Yes. The blue park tool spoke wrench is a perfect fit. And yes the cat managed to fling the toothpick into a crack in the floor. That's why I walked into the garage with 2 toothpicks. I needed another to get the toothpick out of the crack in the hardwood. Nothing stays on the counter or table unless the cat allows it.
Putting the stem in kerosene (oil based) for a few minutes will even more effortlessly clean it of sealant. And doesn't require you to touch the tyre 😉