I had a similar situation a few months back. One observation is that while you’re driving the rubber will be warm and thus reasonably pliable. As long as you keep driving after the puncture it’s no problem.

Once parked overnight they will cool and harden. I drove like that to the dealer to get them replaced but it was a lot less comfortable and felt more ‘squidgy’ for want of a better term.

Safe to do it but just take it real easy and adapt following distances and corner speeds accordingly.