Pilates yes, it's become popular in Switzerland and physios do courses to become pilates instructors. To work as a "normal" physio and to be able to have your work paid by the basic health insurance which everyone has to have, your exmas etc must be approved of. When you are employed the boss registers you so that your work in his/her practicewill be recognised. You have to have your physio qualifications registered and be given the OK. A physio who does Pilates could probably integrate it in the normal day to day work in a practice, or in a hospital rehab setting etc. Having Pilates plus Physio is probably very good but all physios have to go on and have continuous professional development in all sorts of directions after qualifying anyway. Pilates of course could be used by non-physios in private fitness, wellness, health clubs and gyms etc.
The Physio part depends on recognition of exams; then getting someone convinced that they need you AND they'll be able to get a work and residence permit for you AND that you can speak a relevant language. I don't think there'll be many jobs for just english, but maybe you've got another language too?
If you get approval it's easy to put an advertisement in the physiotherapie magazine here and see what comes up.
The approval stuff might take a while to organise, and afterwards each county has slightly different structures for permits. Go thro the physio society for correct information as not all qualified physios and / or students know exactly what is required. People who aren't self-employed themselves haven't gone thro the process of getting a permit for employees. Newly qualified physios do not always get the OK from the central health insurance organisation "Santé Suisse" to work in private practice.
So start finding out and good luck!