Managed it with the VPN app from smartdnsproxy.com (where I already have a subscription anyway, so I can use Amazon Prime Video in Switzerland with a German catalogue).
Start the app, select the German server, then (re)install the Bose app and create a new account with the location Germany, then start the hotspot on the iPhone and connect the portable home speaker to the hotspot (then it also thinks it is in Germany.) Now I could add Alexa.
Then switch to the definitive WLAN via the web interface of the Portable Home Speaker, see the following instructions:
https://www.bose.ch/de_ch...

I managed to set it up, but didn't get any further because the necessary alexa app is not available in the swiss ios store. In general, Amazon Alexa is not available in Switzerland. So you have to set everything up specifically to actually fool the speaker into not being used in Switzerland....