Tip Protector Stuck in Cue Case

Yesterday, I got some tip protectors to keep my case clean. I use a case designed to store my shafts “joint-protector-side up” (tip facing down), and found out the hard way that these tip protectors aren’t exactly snug on the tip.

Now, the tip is wedged deep within the shaft compartment, and tilting or shaking it upside-down didn’t seem to do much. I’m thinking about using a thin vacuum nozzle (≈ 13mm thin) to extract it carefully to avoid damage.

If this idea is not effective or poses risks, what should I consider next?