Phi-Bi

I think the Arceus movie, which was set in an era before Pokeballs (be they made from apricorns or artificial), used those metal harnesses to control Pokémon. They were there referred to as 'magical creatures' or some such. Pokémon is a later term, a portmanteau of Pocket and Monster, and Pokeball is also a derivative portmanteau. Both came to be at the same time, when the method of capturing them in containers was devised.

God, I wish I had a copy of the plot to one of my old Role Plays I made a few years back. I had some clever name for them in a pre-Pokeball era that I was really proud of.

As an idea off the top of my head, you could use the word Beasts with any sort of adjective in front of it like mystic or magical.

^ This. I'm writing some kind of fanfic right now and it's so hard to come up with the correct name. I want it to be a single word though but Beast sounds good~