Do you need to go through the process of writing down your dreams when using WILD or can you just skip it?
Writing down your dreams is important for any method you choose. It increases your dream awareness, which is a key factor in any technique. Writing your dreams down helps you remember them, and if you remember your dreams, you can have many more LD’s because you won’t only be relying on WILD. You can have LD’s through DILD, RCILD, DEILD, and more. Even if you aren’t lucid, normal dreams are still very fun, and they help you find your dream signs. So yes, I’d suggest keeping a dream journal and filling it with as much information as you can. 
If you don’t write down your dreams, even if you do succeed with WILD, it won’t be vivid at all.
Writing down your dreams makes your dreams more vivid, and helps you gain control. Writing down your dreams is a fraction of the effort you need for WILD, anyways.