I would suggest setting aside a stick (maybe even a chopstick!) just for practice, and if you ruin it sharpening one end, learn from that experience. You can cut off your mistake giving a new end to reshape and sharpen. A single stick will provide a lot of ends for practice.
Wood has a grain. If you look at a piece of bare wood, you'll see 'stripes" which come from the annual rings of the tree as it grows - that's the grain. If your's are typical hairsticks, most likely the grain is along the principal axis (iow parallel to the length). You want to sand the wood parallel to the grain. Sanding wood across it will tear it up, leaving a very rough finish.
Before buying sandpaper, you might first try something you probably already have: an emory board (nails).
The emory board has a coarse side and a fine side. The coarse side will remove material more quickly but will leave a scratchy finish. It's best used for rough initial shaping. The fine side will remove much less material per stroke but leave a finer less scratchy finish.
If your final finish is too scratchy, either still catching hair or looking too rough for your eyes, you might try coating your work with some clear nail polish for a glass-smooth finish. Oil, wax or lacquer are other possiblities.
For sandpaper, you don't need wet/dry paper (used for autobody repair and knife sharpening) nor emory paper. Just plain ordinary common sandpaper for wood probably no coarser than 100 grit nor finer than 800 grit.
HTH
PS I love the guy on your head!
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