Merchants on the Shopify Plus plan do have the option to modify the checkout experience but things like amount of steps or order of steps must remain as is. There will also be some fields deemed required that you would not be able to remove.
So the first question to consider: is your client on the Plus plan? The Script Editor is a Plus tool but it is build to handle things like discounting (and some mods to things like what gateways or shipping options show).
Everything before checkout you'll be able to make whatever you like.
★ I jump on these forums in my free time to help and share some insights. Not looking to be hired, and not looking for work. http://freakdesign.com.au ★