Scott Haugen is an outdoor writer and you have probably seen his articles or television shows at some point. His father is alergic to fish and still took the time to take Scott fishing all the time while growing up. Essentially the reverse of your problem. He wore latex gloves to handle fish the times I have fished with them. He is a fanatic fisherman.

I seem to remember he took a course of alergy-blocking shots available to reduce or eliminate the response to some alergens. Fish alergies probably vary quite a bit, but if he has a treatable variety the docs ought to be able to tell.

Good luck with all that!
art