Unlikely to get rabies from a mink, ferret or weasel. According to the DEC only nine cases in a ten year period compared to 175,000 documented cases in raccoons and foxes.
Since mink feed primarily on fish and waterfowl, it even less likely for these critters than weasels and ferrets.
I expect minks and weasels get rabies much more often than is recorded - they are small, elusive, unadapted to human presence, and die discreetly and unnoticed. What they eat probably matters less than whether they encounter a rabid fox or raccoon - fox and raccoon prey animals don’t typically carry rabies either.
My husband and I saw the first mink (or weasel of any kind) we had ever seen last week, running across a road. But we see raccoons and foxes frequently. Two years ago a small rabid raccoon walked right up to our dog and bit her, and then bit our daughter when she rescued the dog.