WhatsApp on iPhone: how to switch to a new phone number without losing anything?
It proved trivial:


power down iPhone
change SIM card
turn iPhone on
launch Whatsapp
Whatsapp asks something like "Mobile network changed. Switch to new phone number?". Tap "No"


That's it. All groups, chat history and contacts preserved. My friends see me (and chat history with me) as I never changed SIM card or number.

Later switch back to the original number works exactly the same.

Mind the warning from Whatsapp FAQ: "Please do not swap SIM cards ... frequently, or you will create problems in the verification process." But with two changes "to new and back to the old" in half an hour, I of course didn't experience any problems.