Susu,
I’m not sure exactly which borer you are treating for, but will offer a few general comments.
For beetle type borers which tunnel galleries inside the trees, few insecticides are going to do much once they’re inside. They are protected against sprays. Hence why Rick mentioned sprays haven’t proven to be very effective.
The caveat is that commercial orchards generally don’t have a problem with shot hole borers because they are fairly intensely sprayed for other insect pests at the same time when various beetle borers are emerging from trees. That is, no problems when broad spectrum insecticides are being used. Small non-bearing trees generally aren’t intensely sprayed, so tend to be more subject to beetle borer attack. I rarely spray non-bearing trees except for leaf curl.
The Zeta-Cypermethrin you mention is something I use (in the commercial form it’s called Mustang Maxx). Though not specifically labeled for ambrosia beetles. It’s a powerful broad spectrum contact insecticide which is going to kill any adult beetles not already tunneled in the trees.
But it’s contact ability is going to diminish with time, so I’m doubtful with the current temps that the sprays would do you any good at this point. Depending on the beetle type, they emerge in spring or early summer. I don’t think your insecticide (sprayed now) would give you much residual when you need it.
As Tippy’s chart shows, pyrethoids (i.e. Zeta Cypermethrin) are fully compatible with copper.