I think it’s plausible there is a connection between a grinning cat and Cheshire being a dairy county. But the causation is not necessarily as you propose.
It’s plausible that the dairy in Cheshire picked a grinning cat as its symbol because cats love milk. Ergo, cheese was pressed into the shape of a grinning cat. Ergo, the phrase “Grinning like a Cheshire cat” is born from the cheese.
No, I don’t have any cites for this. But it’s as likely as the phrase developing from Cheshire being a dairy producer, and then the cheese shaped as a grinning cat coming from the phrase.