The photo of your NHS paper is exactly what you use.
Do not understand what a precruise at checkin would be. Lots of discussion about vaccination rules going away. Remember that the rules are not only from the cruiselines, but countries and ports. Every port would need to need to allow in guests without testing.
Your unvaccinated comment is different from testing. Thus for unvaccinated to sail both the cruiseline and all ports would need to allow it.
Not sure that us what you meant