A King Betta is another name for a half-giant betta. The term "king" is just a marketing ploy.. it sounds better than "half-giant".
Personally I would not divide the tank, Kings (being bigger than the average betta) need more room and I'm sure he would love to have a full 10 gallons to himself.
If you have to have tank mates I would go with ghost shrimp, I've never had a problem with any of my fish killing them or them hurting the fish (which I think is an urban legend anyway). The problem with shrimp is they are EXTREMELY sensitive to water conditions so a cycled tank is a must, even then they don't tend to live very long.
*Be smart.. Do your research!!*