My experience has been that then Japanese do not put a finish on most chop sticks, they throw them away after using. I know that some are, somehow or in some way, saturated with protective oil, but they do not look like they have a finish. They often have their own personal chop sticks (with urushi finish) that they sometimes carry with them or for use at home when they have guests. Some of the chop sticks can be very expensive and these are well decorated. I think they use the same lacquer (urushi) that they use on dishes and bowls, and it is far more durable than most all other finishes, period. IF giving to use for eating, it needs a protective finish or saturated with oil and dried for a while. If used for cooking, unfinished. That said, some oily woods like ebonies, teak and a few others - these oily woods will not take a finish well, unless one is very experienced. If using this kind of (oily) wood, just make it without a finish.
I remember seeing many chop sticks (for use with eating) made from teak, which is dense and oily and buffed. These had decorative finishes only for the top half and buffed on the bottom half.
FYI - Did you know that one (non-Asian) can tell the difference between Chinese, Korean and Japanese by the way each hold and use their chop sticks? Usually, the location of the grip, the different grip styles give them away.
I should also say that different regions within a country, there were differences in use style and choice of chop sticks.
The Japanese language was difficult for me but I learned it! The cultural styles and difference between regions intrigued me immensely. My Japanese friends helped me and liked the fact that I was naturally interested in those cultural habits within regions.