A handler, rider, or trainer, these all terms refer to the same thing: The one taking care of your Kukuri.
Now, handlers are the most free things about the group. The only requirements are that your handler has at least one hand, and passes the smaller handler size shown above. This doesn't have much lore-centric reason, as Kukus can be trained to be docile and thus handled even in smaller sizes, but anything smaller than that would be hard to see in the images, and thus some thing requiring a handler may be impossible. A handler can be smaller than shown above, but they will not NOT be passed as handlers in official images, nor will you get the handler FP bonus from it.
The exception is when the Kukuri has the mutation "Miniature." In pictures only showing and concentrating the miniature, a smaller handler is passed as long as it's smallness is still relative to the char provided above.
Your handler does not have to be a human, they don't have to walk on two legs, and they do not have to even speak English. They can be other closed species, your own species, or anything you desire as long as they follow the two rules given above. They can even be shapeshifters, as long as one of their forms has thumbs.
One Kuku can technically have as many handlers you wish them to have!
When handler is required in activity/training/etc., it does not have to be the handler listed in your Kukuri's import to count as a handler. Any character that qualifies as a handler is counted as a handler.
A handler in activities can be replaced with a starter.