Is it possible for a sole proprietorship to remotely switch to a simplified taxation system or...?

You can change the FOP taxation system through Action - https://diia.gov.ua/services/zminennya-danih-fop. To do this, submit an application online through the tax "One Window" program (form code - F/J 0102003) or send a scanned application through the Taxpayer's Electronic Office (section - Correspondence with the DPS).

You can also contact the Taxpayer Service Center at the place of registration of the FOP.