Many of the paid positions working with animals require one of the Swiss diplomas - would you consider getting Swiss qualifications? You can read more about the various possibilities on the Schweizerischer Verband für Bildung in Tierpflege, here: http://www.tierpfleger.ch
Depending on what you wanted to do, there is the possibility of 'Quereinsteig', a shorter course for those who are pursuing a second qualification - this assumes that you bring experience to the table, which it certainly sounds like you do.
You can also see a list of current job offers - browse these to get an idea of what is available in the field.
Another possibility would be to work towards a diploma as a Tierartzpraxisassistant TPA, what we would call a vet tech in the US. http://www.gstsvs.ch/de/beruf-tpa/ausbildung.html
I've heard that these courses are very competitive to get into, as are jobs once you have the diploma. But perhaps worth checking out.
Now in the mean time...
As Medea suggests, call all the Tierheim and ask if you can volunteer - Swiss experience, building a reputation in the field will help you. Not to mention helping the poor homeless critters - good karma all around.
Another possibility - how about establishing your own pet care business?
As you can see from the many, often desperate, pleas here on EF, there is a great need for skilled, experienced, trustworthy, and rock-solid reliable pet care providers.
There is also need for someone experienced with and willing to take on 'special needs' pet - pets with medical conditions or behavioral issues.
There are only a few petsitters who fill this niche today - most will not care for 'special needs' pets. But if you have the skills to do so, if you set yourself up correctly (from a business/legal/tax/insurance standpoint, offering care in the client's home or in yours, as needed) you could likely be as busy as you want to be.
There are no education requirements if you care for cats or other small furries, but if you offer care for up to 5 dogs at a time you will need to do the SKN courses, the same courses that every owner must take. These are very easily done, and inexpensive. Offering care for more than 5 dogs requires either the FBA or the Tierpfleger diploma, see the first link. You can read more here: Requirements For Dog Care Providers
Key would be to set yourself up correctly. A good many pet care providers are working illegally, which leaves the client in a very risky position. If you set yourself up right, you could do quite well.
Wishing you all the best.