The only flaw is the assumption that the disabled person can read or can read English (assuming you're publishing posted sign in English only). is it possible / likely / forseeable that the tea-room could attract customers who cannot read, or cannot read English?
There is no easy Pictogram route out of this that I am aware of.
Nor, am I for one second, proposing a sign the size of billboard with every language known to mankind repeating the message, but the possibility of a sign being missed / misunderstood could throw your strategy into disarray.
as for being OTT, no, I don't think so, you're facing the normal fire safety problem that access does not always = egress especially for persons who require assistance to use the egress route.