Mesmer Dye?
So I do not have the answer, but I have a suggestion:
- take a picture with a mesmer and find the color you look for (for example a color in the GS 1 beam)
- get the RGB or hex value of this color. For example I found F4B8F9
- then use this link (they may be some better ones) to find the best matching dye http://pendion.nfshost.com/gw2/dyesearch.php?h=F4B8F9
This link (https://www.gw2bltc.com/tool/dye/search?cloth=f4b8f9&ipg=25&page=1&sort=cloth) seems to be better in the sense that they also include the material, but unfortunately, I find their match not to be as good. But it still helps.