Yeah, CA glue gives off fumes as it cures, and it's the fumes that can etch clear styrene.
I use styrene cement, or white glue, depending more on immediate availablity (is it in reach?) and how easy or difficult it will be to apply the cement.
For styrene cement, I've used liquid cements, starting with Plastruct Weldene and Bondene, then graduating to Testor's in the odd-shaped black bottle, and finally to Tamiya Extra-Thin. I also use Testor's styrene cement in the tubes.
I like to use white glue when there are gaps around the clear bits, to help fill those gaps.