Hi @bas.hopstaken,
The problem is that NACE code is an focuses on where in the industry a company is working and KVK and VAT is a number for an actual company. What you need is an database that includes your list of companies and it can give you back NACE for each and every company you have.
I come from the industry (DNB/Bisnode) where that information is sold. I never stumbled across such a data source that was actually good (or even bad).
I would recommend reaching out to Dun & Bradstreet or Bureau van Dijk (these are the two global players but local ones exist of course). The will do a one time data cleaning for you and it will save you time and it’s not that expensive (or ask them for a trail account in one of their tools, but they of course try not to give you a data cleaning for free).