Dorothy, assuming you are UK based, the museum should have had a fire risk assessment (FRA)completed. This process must consider the needs of vulnerable people who may resort in the premises, and of course access to the general public will mean persons with variable disabilities may be present
It is really difficult to know the solution re the fourth floor issue without knowing much more. But the FRA should have the answer and lead to an emergency plan for the building which must encompass all persons. If you cannot evacuate all persons from the mezzanine , then you should consider restarting access immediately - ie tomorrow! - until a solution is agreed and implemented.
The first steps might be to look at the FRA and if the details are a bit scarce, I would recontact the person who conducted the FRA and ask them. Alternatively, a review of the FRA should be triggered by your findings
Whilst Covid was absolutely a good reason to cancel fire drills in 2020, the status of covid restrictions in the UK right now is not suitable to justify not completing a fire drill, especially in a high risk premises where members of the public may need to be escorted or assisted - even by showing them the way. I would be very careful as fire safety enforcement teams will expect drills to have resumed.
Fire drills can indeed be announced to staff in advance. I am a great believer that where staff are informed when the drill will take place, and they are told that questions will be asked during the drill to check staff understanding of the procedures, most staff (certainly managers) will immediately look up what their role is or what the procedures are as nobody wants to look a fool.
Plus a drill is an extension of staff training, so why set up a scenario which may fail? Nobody learns, and some will be humiliated - that is not a great way to ‘sell’ fire safety.
I can also see no reason why you cannot carry out the drill out of hours - i.e. immediately before or after business hours as to train staff, check processes, but not to inconvenience clients. However, the fire drill process should really be determined by the FRA & emergency plan.
I have worked at sites where fire drills are not possible in a conventional sense as a process being carried out must not be interrupted. Instead a programme of table top exercises for small groups of staff were carried out, along with ‘walk and talk’ briefings during a tour of the premises. So some flexibility is possible and if your FRA states its acceptable to do a drill with no clients, then this maybe the way to go
Please do come back here and let us know how you get on, but I really do urge you to restrict the 4th floor mezz level as soon as possible. Delaying due to anxieties over discrimination could lead you to further hot water with fire safety legislation!!