Had a similar issue with non standard wheel colours.
The way forward is to find who has a paint scanner e.g. PPG Rapidmatch (Chips away franchise use this). This will need a flat area about 40mm square ideally to scan the paint but you can trick it into doing it over smaller areas with a less accurate result. My local paint supplier had a scanner and do it for free.. presuming you buy their more expensive (But better quality) paint

. I have just used a paint pen from Halfrauds etc for small chips; they usually let you waft in/out checking colours to get a fair match .. Of course you could just let the trades do their magic..
.. my result on my non Mazda was "Mazda steel grey mica metallic".. which is a good match. The material to paint a metallic finish wheel would be £20 at least so £50 is cheap .. min colour mix is about £12/0.25 litre of paint. It cost me £200 to find a used 18" rim, chemical dip and sand blast, fix the fake rim bolts, get the wrong colour plastic coat, and finally DIY the paint job so sounds like you had a decent result.