From the way things looked, the Sharlin had nothing particularly special about it, except perhaps that its crew was likely the best in the entire Minbari Federation...
Why would you make it different in the first place? That just draws attention. The best defense is to make your ship carrying the entire leader caste look exactly like the other 200 Sharlins right next to it. How could you tell the difference? If anything, at most, the Grey Council's Sharlin would feature increased C3 (Command, Control, Communication) equipment, and better stealth generation... at most. And likely, that would be a feature of "Command" variants of the Sharlin in the first place (Like the Black Star). However, it seems all Sharlins have increased C3 capabilities, likely so they can serve as flagships in task forces made up of larger ships (You see evidence of it in one episode where Sheridan leads a battle from the Sharlin's command section) so... conclusively, the Grey Council's Sharlin, beyond crew, is no different from any other Sharlin.