tl;dr Alex created a tool which shows your current skins and dyes on your characters. https://wiki.guildwars2.com/wiki/User:Greener/Appearance
As a person who's reluctant to change skins and dyes for fear of never getting back what I had, I asked Chieftain Alex to work some magic and build a tool for me. He went well above and beyond my expectations, and I can now backup my characters' looks before I start changing things around (I'm currently dropping the information directly into Excel).
If you'd like to backup your characters' appearances too, all you need to do is generate an API key which has 'Account', 'Character', and 'Inventory' checked, and then copy/paste the API key into the box on this page and click "Apply". All of the information is held on your browser side, which you can clear by clicking "Forget stored key". No account information is stored on the wiki, and no one on the wiki can access it.
To generate an API key:
1. Go to: https://account.arena.net/applications and log in. The site belongs to Anet, as per the URL if you're worried.
2. Click "New Key" and select 'Account', 'Characters', and 'Inventory'.
3. You'll be given a very long string of numbers and letters, which is your API key.
This key is acts like a permission slip so that you can access only the selected information on your account. At any time you may delete this API key, which will permanently remove its permission.
If you found this tool useful and you'd like to thank its creator, feel free to pass on your appreciation to his talk page.