I don't know if you realize how unrealistic you're being.
Exotic, no math or science. Only involves birds and cats.
Well, there is no kind of work you can that doesn't involve math, and only involves birds and cats.
Most any work these days involves using a computer - in a pet shop or vet's office, to check the customer in and out, record what services and goods he's bought, set up when he should come back and send out mail, etc. You have to be able to look at the results the computer gives and know ball park, what the result should be, so you can check the results.
Working in a pet shop or as a vet tech, you have to know about fish, cats, birds, small animals, feeds, plus you have to be able to do math to do inventory, check sales receipts, cash out, etc.
If you were to work in a zoo, it would be exotic, and you'd be around birds and cats (some of them fairly large), but I think you'd be a glorified janitor. They don't let people handle exotic animals unless they have training, some sort of education. The schedule might not be that different from a family business - people work weekends and holidays at a zoo.
You'd also be expected to keep very detailed records about the animal's care and know when to notify the veterinarian. You're in the public eye a lot and expected to communicate well and be polite to the public. These are extremely valuable animals and you don't get jobs like that so easily.
The key to exotic jobs, doing what you want, is education, and mostly in math and science. You don't mention if you have any college training. If you don't you might want to get some.
That can be the trouble with a family business. Many people go into the family business right from high school, find out they don't like it, and come out without the education that makes them competitive in the job market.
There are two year programs at community colleges in animal science and agriculture that might help you get closer to doing what you want, but I don't think there is any job that is going to be perfectly fit to these expectations.
Animal science, even just the two year program, what you'd have to study to be allowed to work around animals, means SCIENCE. Biology, chemistry and math. Not four years of biology, no, probably two terms, and beginning chemistry. I was in the animal science program before vet school, so I speak from experience.
I don't know why you're so totally against learning science and math. They are the two keys to many good jobs. I didn't like math and science either, but to get what you want, you have to do some things you maybe don't like as much.