Not being familiar with American weasels (and this article shows it has nothing to do with 'fish'), the only time I have heard fisher is as a common surname, both in England and in Germany (as Fischer), and when I was made to read the Bible at school:
And he saith unto them, Follow me, and I will make you fishers of men. (KJV Mt. 4:19)
I note also what Wikipedia says
Fisher is an archaic term for a fisherman, revived as gender-neutral. D
One of mine actually. And despite having 'Fisher' it sounds wrong but clearly wasn't not long ago in the UK.
And DaibhidhR, we have fishers in the area. Small, similar to mink. Definitely fast swimmers and could get a food out of a lakeshore or river if they chose. I know the raccoons get the blame for all the empty clam shells...