My two cents
The first thing to know is that in Switzerland, there are basically three languages that are spoken in three different regions: German, French and Italian.
In big cities, where most universities teaching Service Design and companies hiring service designers are, many people speak English too.
So yes, you can perfectly live in Switzerland knowing only English, but it definitely helps to speak the regional language.
It might be easier to study knowing only English, as there are some programs where English is the main language, like the Master Program in Service Design of the HSLU in Luzern, than to find a job that is willing to hire someone who can't speak the local language.
So yes, you can live and study in Switzerland not knowing the regional language, but it might get hard to find a job.