Question about The King of Shreds and Patches Puzzle

I tried to make the title vague enough so it didn’t have spoilers but also descriptive enough to mean something.

When you enter Traitor’s gate on the 21st, a bunch of cultists arrive. If you make yourself known to them, they will get suspicious of you. I know how to progress from this point. My question has to do with something else.

If the leader sees you, he will say: “You are not dressed properly for the ceremony, brother.” I was wondering if it was at all possible to dress properly. I tried dressing in the wig, lucy’s cloak, with the pin, the old boots, and a sheathed rapier in the sword belt, but it appears that wasn’t proper. I will try other combinations, but I remain doubtful. Does anyone know if there’s a proper way to dress for the cultist?