It depends on how wide the space between the tines is. If the space is very small, fold and tear* the sandpaper into strips so that you can place the sandpaper between the tines and hold it on either side comfortably, brace the comb between your knees or use a vice/clamp that is padded so it won't scratch the comb so you can use both hands on the sandpaper. Move the paper back and forth and up and down the tines.
If the space is wide enough, wrapping the sandpaper around a strong object that fits in the space will make smoothing the area where the tines meet the body of the comb much easier, especially if the object is the same shape as that gap (but smaller) so you can really reach all surfaces. If you happen to have a hobby model shop nearby, they should have very small sandpaper rods for getting into tight spaces, but you can improvise well enough. Think about what you have on hand between the diameter of a toothpick and a pencil.
For grit, 220 should do the trick, but depending on the amount of roughness, if it isn't smoothing down fairly easily starting with 120 or 180 will make life easier. 220 is "smooth enough" for hair but I prefer to sand to a minimum of 320. For a noticeably polished surface, progress through 400 and 600 grits as well.
*Folding back and forth a couple times usually makes the sandpaper easy to tear in a straight line, you can also use the edge of a table or similar.
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