I am looking to mark individual crayfish in an aquarium filled with water, but don't want to cause a change in behavior by marking them with something that they will chemically sense and react to.
I would use RFID chips to mark them, depending on your animals they could be embedded in tissue or externally. This would be suitable especially for high numbers of animals. There are a number of different RFID tagging systems out, if you want I can recommend you some.
More cost-effective, but maybe only for a smaller number of individuals would be marking by punching holes in the uropod. Theoretically it allows a high number of different individuals, but in practice I think applying the system and identifying the animals takes more time. Check out the paper by Rui Zhang Guan, 1997, An Improved Method for Marking Crayfish.
Small, numbered plastic tags attached with cyanoacrylate glue (super glue) works well. I've had better success with the gel-type glue for this kind of application, as regular super glue is very runny and hard to control. You can purchase numbered bee tags, or get the sheets/strips of numbers used by electricians to mark wires. With the latter you'll get a lot of copies of the same number, but you can make them different colors with waterproof pens (Sharpies). If you don't need really tiny tags, you can laser print your numbers on acetate film and then make round tags using a hole punch.