Even if the TZConnection has no connection string property you can set the additional connection parameters in TZConnection.Properties.
I presume you run your MySQL server this way
mysqld --skip-networking --shared_memory=1 --shared-memory-base-name='MyMemoryDB'
To enable your shared memory connection you might try to add the following configuration lines into the property TZConnection.Properties at design time in Object Inspector.
Note that the protocol must be set as it is and shared-memory-base-name to the same value as you used in the command line parameter. The default value is MYSQL so if you omit the parameter in command line then you should change the following MyMemoryDB values to MYSQL.
So in TZConnection.Properties property try to add these two lines
protocol=memory
shared-memory-base-name=MyMemoryDB
or at runtime in the TZConnection.BeforeConnect event handler use
procedure TForm1.ZConnection1BeforeConnect(Sender: TObject);
begin
ZConnection1.Properties.Add('protocol=memory');
ZConnection1.Properties.Add('shared-memory-base-name=MyMemoryDB');
end;
Hope this will help you somehow. I haven't tested it because I don't have the proper environment.