Depending how small you want there are lots of knives that will do what you want. Many are also acceptable in restrictive jurisdictions.

Some suggestions:

Fox Vulpis 1 penknife. This is high quality, good materials and unlikely to scare the horses.

Kizer Walnut. It has an unusual look, but it works well for the sort of light duties you are looking at. More likely to intrigue onlookers than alarm them.

Lansky Madrock World Legal. This one might catch the professional interest of police and get you side-eye at the school gates. It looks a bit more aggressive than the previously mentioned knives. It's a bit bigger too, but still a small knife. The Hawksbill blade is probably the best for box cutting and will sharpen a pencil just fine.

The Svord Peasant Mini or Micro. These are bloody great, fun knives. Get one of these. They look like and are perfectly normal working knives. Not zombie apocalypse weapons, just tools. The police may want a look but they won't get alarmed. Brenda at the school gate may still think you are weird, but not an unhinged murderer. The peasant knives will do what you want. You can sharpen them with the most basic tools and you'll learn to do it decently. Just get one, everyone needs one eventually.

I do have a favourite but I think I've been pretty even handed.