Put some vinegar in the blocked chamber.
Then add a little bit of baking powder or baking soda to the vinegar.
Then quickly block the chamber mouth with your finger.
The pressure from the CO2 bubbles will build up which could force the wood to back out of the hole.
After a few minutes, rinse the solution out of the chamber and repeat if necessary.
Here's a link about it and there's also videos about it on youtube, --->>>
https://www.wonderopolis.org/wonder/what-happens-when-you-mix-vinegar-and-baking-soda#:~:text=When vinegar and baking soda,carbonic acid and sodium acetate.&text=This creates the bubbles and,mix baking soda and vinegar.
A similar idea would be to put a grain of powder into the nipple before capping it and trying to fire it out.
The difference between the 2 methods is that using the percussion cap with powder, you're trying to force the large end of the wood through a small hole.
Whereas by using the vinegar and baking powder, you're trying to back the small tip of the wood out of the hole in reverse.
Even if you burned the wood with a lighter, the carbon residue may still end up blocking the hole.
The vinegar solution can help to open the hole as well as using a grain of powder and percussion cap.
Both methods would be used together to get the hole open since the vinegar would act as a softening agent.
If you can find a thin enough paper clip and straighten it out by removing the bends, it might be stiff enough to be used as a nipple pick.
Or go to a guitar shop and see if you can obtain a stiff piece of guitar string, piano wire or music wire.
If there's a piano tuner in your area, he would have some.