Spyderco or Gerber if you want a lockblade w/o assisted opening. They are designed to open and close one handed. Kershaw if you want the assisted opening.
Personally, I like a more traditional pocketknife, because they tend to cut better, and I like how they look and feel better. I have had to learn to open and close them one handed when forced by circumstances. The Case Copperlock is one that is easy to open and close one handed. Can pinch the blade and snap it down, or grip the back of the handle between the lips and pinch the blade open with the fingers. Non-lockbacks are fairly easy to open one handed, especially if they are single-bladed, by doing the same method of gripping the handle by the lips and then pinching the blade open -- that method requires enough blade above the handle to pinch.
I would not give a 10yo a switchblade to carry around. Maybe just to play with and have for when he gets older, but for now, it would be a more conventional, low profile pocketknife. Butterfly knives are one-handed tools, as well, and while it would probably be fine to give it to him to have, I would still have reservations about him carrying it. Benchmade model 42, if you go that route.
Heck, you could just get him a small sheath knife, like the size of a paring knife, or even an Old Hickory paring knife -- less to worry about opening and closing then, and nobody should hassle him about it.