I don't know if this what your looking for but Testors makes a clear plastic cement for attaching the plastic windows to buildings . Drys clear and can not tell where the cement had been applied. Later RJD
This is a difficult problem because the materials are so dissimilar and the wire is so thin that you do not have much surface area to adhere to.
My normal answer is to use E-6000 to glue metal to plastic. This might be a little messy in this application. It sounds like you were using some sort of Super-Glue ( CA ) and that is why your clear parts were fogging. Besides the fogging, was the glue you tried working for you. You can get CA glues that are supposed to not fog clear plastics. They should be available at your local Hobby Shop. Also, I've heard that coating the clear plastic in FUTURE Floor Wax will prevent the fogging.
How large of an area are you gluing? How strong does it have to be?
Assuming you're attaching the wire flat to the surface of the polycarbonate and not really knowing what you're trying to do.......
Can you solder small pegs made of the same wire along what will be the backside of the wire? Then drill holes in the polycarbonate for a tight fit for the pegs. A small amount of cement in the holes should be enough to hold the pegs in place. Too, it would be possible to have the wire a small bit off the surface of the polycarbonate if desired as well.
Actually, what I'm doing is making glasses for my figures! I figured out a fairly easy way to make glasses that requires gluing a very thin copper wire lengthwise along the edge of a very tiny piece of polycarbonate. The thick CA I used worked fine but left the plastic very fogged, which detracts from the effect.
Omni-Stick. It is clear and dries clear. It is similar to E6000 but is thinner and clearer. From the little I have used it, it seems pretty good. It was recommended to me by Jeff at Shawmut Car Shops. He uses it a lot.