Mind you that today's regulations are pretty strict, I've seen near zero VOC but given zero, well, I'd get with https://en.wikipedia.org/wiki/IPC_%28electronics%29 and ask for advice.
Some pressure sensitive adhesive might do the trick.
I am researching to find a VOC-free adhesive to secure some wires to a PCB so as to get them out of the way for packaging. Hot glue is the current method however it is messy. Are there any more reasonable alternatives?