You can only use "welding cable" as a NEC wiring method if the cable has an additional listing of a type shown in 310.104 and then you have to use listed termination products for the fine stranded cable.
Generally speaking it's a "no go"
We use Type W cable for a bunch of Navy experimental systems, but they are "cord and plug" connected with large pin/sleeve connectors, so not a Chapter 3 method.