3M Professional Chip & Scratch Repair Kit

You'd have to remove the wax to get the Zaino to bond. The "Shine restorer/wax" is likely an all-in-one product that does some polishing with fine abrasives and adds protection with wax. You could use a separate polish instead with no protective component, and then follow it up with Zaino. However, a good polish will cost nearly as much as your chip repair kit. For instance, a bottle of Menzerna Final Polish II is about $16. I'm guessing the reason they package it together is that you will still have fine scratches in your finish after using their kit, and the carnauba wax helps hide them, as it is much better than any sealant (including Zaino Z-5 Pro) at hiding swirl marks.

You could just use the kit as-is, then wait a month or so for the wax to wear off on its own. You can even help at the end by washing your car with Dawn liquid dishwashing soap. But like I said, you'll probably find you have fine swirls where you applied the rubbing compound and shine restorer, and they'll be more visible when you use Zaino compared to a carnauba wax.