Poke the branch with the wire you intend to use.
What moves/gives; the wire or the branch?
If the wire bends, it's not thick enough.
Generally a wire 1/3rd the diameter of the branch works.
You may have to double up or pair your wires if necessary.

Thanks, do I get copper wire, or does it matter??

I'd be careful about wiring trees in the ground. They grow fast, and wire can cut into the branches quickly. What exactly are you trying to accomplish with these trees?

Chris Johnston

Here is a link that might be useful: Sashi-eda Bonsai