I believe that the exemption of doorsets from the Insulation criterion was, as had been said, mooted because of the assumption that doors wouldn’t have combustible stuff placed against or in front of them (otherwise they wouldn’t be very useful as doors) and also, I believe, to deal with the fact that in ‘olden days’ you could only get non-insulating f/r glass, so if you insisted on insulation performance you couldn’t have vision panels in doors. They probably also didn’t want to ‘legislate’ against steel fire doors & roller shutters (which are really difficult to design to be insulating). That still applies today, though we do have limitations on the extent of un-insulated glazing in Table A4 of the E&W Approved Doc B.
So... if one could satisfy oneself that the same assumption could be made, & if one were confident that the wall-coverings were specified so they wouldn’t ignite if the metal got hot, & that the contents of the safe were likely to be substantially non-combustible, then I’d have thought you might be able to make the case. I’m not sure detection is much of mitigation – when considering trade-offs against F/R detection is only really useful if it means something subsequently happens to keep the fire small or to put it out - & I’m not sure you could make that argument here? On a hospital street I think you’d have to assume that escape could be a drawn-out process, so it’s one of those places where I always regard reliable fire resistance as being really important.
If you did decide that you wanted to insulate the safe then I don’t think you could do much better than line the aperture with a 2-3 of layers of plasterboard or something else made of gypsum. Gypsum has lots of water chemically bound into its molecular structure, which will never become liberated at room temperature but in a fire it gets hot enough to be released. The plasterboard cannot physically get above 100 degrees C until the water in it is driven off – so it’s very good at keeping the things behind it cool, until it becomes completely desiccated (better than some of the specialist f/r boards). You don't say what the wall is made of - I'm assuming it's masonry? If it's dry-lining then I would be worried about the installation wrecking the F/R of the wall, fire stopping or no fire-stopping.