For "makes your coffee white" there is already the established product name "coffee whitener". What's wrong with using that one instead of mislabeling it as a dairy product?
For most of those things that aren't milk, the answer is "no". So they aren't milk alternatives, are they?
Honestly, if someone told me that they got confused between dairy milk and plant-based milk, I'd laugh at them. It's not likely to be a recurrent problem either, as surely you'd realise when you came to use it.