Disclaimer: Yes this Topic has been discussed many times before, the point of this post is my recommendation on how it should be done:
To keep it simple, after dragging a dye onto one of your character parts, whether that’s your weapon, helmet, torso etc. there’ll be an “Are you sure you want to Dye this equipment?” like when throwing out a Soul-bound item (not sure if this is already the case:
As your character is actively previewed whenever you remove equipment or add equipment I don’t see why it can’t preview the dye’s you want to apply on yourself as well:
So after dragging a piece of equipment onto one of your character’s slots and when it asks for you to confirm the Dye it will also TEMPORARILY be previewed in your inventory-screen.