Now THIS is an interesting question!
Probably depends on the characteristics of the trainer in question and what other objects are banned/controlled by the law in that jurisdiction.
For example, I would think any rubber or neoprene (ie. "soft") training knife would not be considered a weapon. However, how "real" does it look, and where are you taking it? I doubt it would make it onto an airliner nowadays, for instance. And in the dark, the "authorities-that-be" may claim you could use it to threaten someone with. Keep in mind there are restrictions on TOY GUNS in some areas!
However, aluminum and wood trainers (ie. "hard") might not be considered "knives," but could be considered "yawara sticks" or something of that nature. And yes, they CAN hurt someone, even though they ain't knives. Look at a bokken. Or even a wooden tanto. And those aluminum training knives can still pack a wallop and they increase your reach--sometimes by a good margin. The edge of a quarter-inch thick, eight-inch long bladed aluminum trainer could possibly break hand bones or bust up a nose pretty well. Possibly break an arm bone, especially at the wrist.
I don't think it would be going too far to guess that the folding training knives could be considered "folding yawaras."
Never underestimate the rabidity, resourcefulness, and willingness to stretch the law of tyrannical authorities...
Karl
