I also come from a non-EU country. The company I was working for was localted in Thurgau, this company left to Germany, as I decided to stay in Switzerland, my employment contract was cancelled upon agreement. Later on I found a job in Zürich, it was no problem to stay in Kanton Thurgau while working in Kanton Zürich. About 2 weeks ago we moved to Wallisellen (Kanton Zürich), we did the abmelden (de-registetration) in the gemeinde of Kreuzlingen and the anmelden (registration) in Wallisellen, it was very straight forward, just fill up some forms, copy of the contract of the apartment, copy of passports and our B-Permits. Funny though, was that they didn't ask for my employment contract, I guess it was because on my B-Permite from Thurgau it already stated my new employer. At the Gemeinde they said it will take maximum 3 months (because of Kanton change). Till now I dont even know if they have contacted my employers for asking a confirmation of contract.

All I can say is that in my experience it has been very straight forward.

The only risk you have here, is that you dont pass the probation period. In my case Kreuzlingen to Zürich was 1 hour drive, first I made sure I was secure on my new job and then I moved. If possible, I suggest you do the same.

Greetings