Its a personal choice to not carry a phone. While it could be helpful in some situations, it seems to be a conscious choice so thats up to the OP.

In any case the OP will be helped at the transfer desks in Amsterdam. Either through the machines if the automatically rebooked option is suitable, or by one of the agents. That is if there actually would be a need to rebook - chances are that the flight will operate normally of course

If the flight gets cancelled or heavily delayed from MAN I would recommended first talking to the AF/KL crew at MAN for a possible rerouting. They may be able to re-route you via Paris or another gateway that offers Japan flights.