Good on you for trying to help your wife - we live in a society where our space is shared with animals, so this kind of phobia can be crippling.
Is your wife 'simply' afraid of animals, or do you think the fear is at the phobia level?
The first you can likely help her to overcome by introducing her slowly and carefully to appropriate animals as suggested by other posters. Petting zoos are often a good place to start, as the animals are generally acclimated to interacting with people.
But a true phobia often requires professional help. And by professional, I mean trained animals as well. Honestly, if your wife's fear is a true phobia I would not tackle this on my own - I would look for help from folks who have both training in animal behavior and in human phobia management.
It is critical that you ensure that any interaction your wife has with an animal is a good one - which means choosing the event and the animal carefully. In the case of phobia-level fear, you would likely need to work with animals who have been specifically trained or who have been assessed as having the right kind of character and (species-specific) behavior to work with someone like your wife. Working with the wrong animal could make the problem far worse.
A difficulty in addressing animal phobias is that unlike some common phobias, the trigger is a sentient being - and so treating the phobia requires care for and from both parties.
There are several therapy programs involving animals which would be appropriate to your wife's needs. What sort of animal do you think she should start with? Dogs? Cats? Horses?
I don't know much about the Swiss animal world outside of Dogdom.... but if you wished to tackle the problem first with dogs, perhaps contacting one of the Hundetherapie groups might be a place to start. Therapy dogs are trained to do various jobs (comforting those suffering from PTSD, working with dementia patients, helping autistic children, etc.) so you would need to find a dog and handler who are trained to help those with animal phobia. To get you started, why not write these folks and ask how to find an appropriate therapy dog:
http://www.therapiehunde.ch
My trainer is not only brilliant with dogs, but she is also a social worker. I'll ask her for recommendations for resources for your wife, and get back to you. You might also want to contact EF member Argus; I believe her dog is a Therapiehund, she might know who to contact to find more information.
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A point I feel must be made:
A 'Welpenspielgruppe' as mentioned above is absolutely NOT the place to begin.
First of all, the purpose of such a group is to start a socialization program for puppies - by it's very nature you have a room full of unsocialized, untrained, boingy, rowdy, razor-sharp toothed, pee-ing and poo-ing machines whose 'off' switches have not yet been installed. Cute as hell, but NOT for those afraid of dogs. Sticking a dog-phobic person in a Welpenspielgruppe could result in flooding, and (as with flooding a fearful animal) likely serve to ingrain the fear.
Secondly, a Welpenspielgruppe is not a public event. It is a safe place for puppies to learn how to behave in a human world. A person who is afraid of animals could do quite a bit of damage to the pups. No decent trainer would allow strangers to interact with a Welpenspielgruppe, it would contravene everything the exercise is supposed to do.
A shelter is also not a good idea. Again, the purpose of a shelter is to provide a safe environment for the poor homeless animals. Some of these animals have been abused and so are afraid of people, some otherwise mentally healthy are animals simply are not at their best in the confusion of a shelter environment. A visitor who is afraid of animals can, again, inadvertently hurt the animals.
While I always encourage people to volunteer at animal shelters, one must first be a true animal lover. So work on the fear first - and when you and your wife have overcome it, then consider a bit of voluntary dog walking or cat visiting.
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Although I am a dyed-in-the-wool animal mammal lover, I have to confess: I am both Ichthyophobic and Ophidiophobic. Fish and snakes seriously creep me out. I manage the fear mostly by avoidance; I do not go to the snake house at the zoo, and I avoiding walking by the fish counter at the Coop. But it's easier to avoid fish and reptiles in today's society than it is mammals - so I applaud you and your wife for trying to tackle the problem.