Looking for drill bit tapered to match pencil sharpener
You may have seen a taper reamer, there are a few different tapers. They are made to cut steel so wood is easy.

They would need a 1/16 to 1/8 pilot hole as they do not cut in the center. I have a few from when I worked in a bit factory. I expect they are very expensive to buy.

However, I would drill a regular hole and use a dowel.