There's a cap on the market board called "Dream Hat" that fits what you are looking for, it's about 5k on my server so not expensive .

As for the hat on mogstation, I could see it being a bit confusing however the item description says, "Complete your disguise with this saintly cap and false beard!
When a false moustache alone fails to conceal your identity, try donning this saintly cap and beard. Friends and strangers alike will be convinced you're the Saint of Nymeia himself."