If you are really looking for the thinnest possible, consider stainless steel shim stock. I used to do a lot of work with 0.006", and it comes thinner than that. Would not be especially rigid/flat for a 7" disc at that thickness, but I'm not clear how rigid/flat this needs to be from your description.
A center punch, a compass, a drill, a jeweler's saw and a file would be the bottom end tooling for thicker material. A 1/4" hole punch and aircraft shears might do for shim stock. Not clear from your description how precise these need to be (ie, should they be cleaned up in a lathe, or is that more precision than is needed?) This affects tooling needed.
If you are doing electrolysis with stainless electrodes, be aware that you may be producing/exposing yourself to really nasty chromium compound polluted waste material.
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Cats, coffee, chocolate...vices to live by
Cats, coffee, chocolate...vices to live by