If Lord Keith issued orders on 8th january and the convention was signed on 24 january, there are good chance that the convention did not travel in time from Gibraltar, seat of the Admiralty, to Alexandria : 3.300 km in straight line, at least 10 days for a packet or 20 days for a ship of the line, not considering bad winter weather, potential contrary wind or calm in central Mediterranea, possible detour to avoid barbaresque coasts or french privateers.
I don't know the status of Sidney Smith then, but it was not unusual for english general officers to sign convention with french generals without detailed instructions from their government. Cintra is a good example, and I think the case occured repeteadly in Antillas during the previous wars.
Regards,
Jean