there is no difference between Italian or Swiss power, both are 230V single phase which means 400V phase-to-phase in a 3phase.
the fan you have is requiring 3phase power. the "thing" that you have found is capacitor. capacitor can be used to start certain motor types from single phase (to run motor, you need rotating field and capacitor provides phase shift). this is a small load (200W), without upgrading your home service to three phase, the best way is to use a small inverter. there are alternatives to inverter - all capable to "get the motor running" but may have some limitations (load, speed, power, startup ...).
inverters basically produce 3phase output (and at the same time change frequency allowing you to control velocity of the motor). while most inverters are meant for large motors and therefore require 3phase input, in the recent years there was quite a few low power models that use single phase as power input. i would look on eBay for bargains. inverters are commonly known as VFD or VSD and they are made by many companies (AB, SEW, Siemens, Lenze, Schneider,...). note that VFDs in general need some configuring of parameters (need manual, printed of PDF).