For aluminium bonsai wire is recommended 1/3 to 1/2 of branch diameter. Copper is a bit harder, so probably even smaller diameter will suffice.

Extend about 2" of wire from your hand and try to bend the branch slightly...if wire bends, try heavier...if branch bends- your good. Do it every branch you wire to develop a feel. This is going to be much more reliable as it will work regardless of the degree of stiffness of the specie's branches or type of wire used.

There might be a better strategy - let's look at a picture. Maples scar easily from wire, and the scars show for a long time, which is why most experienced growers use aluminum wire on trees in the Acer genus. W/o seeing a picture it's just speculation, but raffia or vet wrap for protection + multiple wraps of aluminum wire will likely be a better choice than copper, for maples. I'm interested in a picture because you might be able to do something mechanical w/o wire that will serve better.

What I would typically do in a situation like yours is, wait for spring and a small branch to form on the vertical branch. THAT one could then be easily wired into place and the wayward branch pruned off just distal to the little branch you wired.

..... and you're sure the wayward branch isn't being expressed by the understock? Most of the dissectum varieties of maples sold are grafts. Very often, branches erupt from understock proximal to the graft and must be removed, lest they over-take the trees resources.

Al