What we usually do with new shinai(s) is to wax the monouchi part of the shinai. You can buy a colorless white candle and apply wax to the shinai. It gives a degree of protection to the area that is usually the contact area. So it provides some protection. (When waxing make sure no wax droppings fall to the dojo floor, use a cloth or paper to capture the waxing that falls off).
Sometimes I see people apply oil to the shinai but until you have shaved it some, because of splinters or other damage, oil won't really apply to the top skin of the bamboo, only when sanding those areas will oiling be beneficial, then it covers the scrapped area.
Kendo-Guide.Com: I do not recommend waxing shinai because it makes mess on the floor as mentioned above, and also on people's men and do. Waxing was popular when I was a youngster but oil is more preferred now due to those reasons. You can buy oil for shinai online too.
Oiling shinai on the surface does not really do anything because bamboos absorb oil through nodes (joints of bamboo). So some people buy a few shinai at a time and place oil-absorbed cottons/tissues inside a shinai on the joints of bamboos and assemble it together and leave it for a few days. Apparently it takes about one month for oil to go through the entire shinai. So you can leave the cottons more than a few days.
After sanding a shinai, you probably should apply some oil on the sanded part of shinai but do not sand the flat shiny part of shinai too much since it is already coated. If you see cracks/splinters on the flat surface of your shinai, it is quite likely that the that piece is broken inside. You should take the shinai apart and check if there are any cracks.
I thought I wrote an article on oiling shinias but I cannot find it. I should write an article on this matter.
