I found a few raesons why all signs point to it being an axe.
1. They probably called it the keyblade to make it sound cooler. I mean it keyaxe wouldn't sound too good.
2. the dictionary says that a sword is "a weapon with a long, strait or slightly curved, sharp edged on one side or both sides with one end pointed and the other side fixed to a hilt" and it says that an axe is " an instrument with a bladed head on a handle or helve". Compare these two and see which one the keyblade relates too.
3. look at these pics (first is a kingdom key, then a sword and then an axe) and tell me which two look more alike.