LiveAquaria.com suggests a minimum tank size of 120 gallons/454 liters for a mimic tang. Your tank at 105 gallons/400 liters is a little smaller, so I would be concerned about the possibility of aggression. I don't have any experience with the mimic, though.
I would probably forego the mimic, as I really don't like pulling apart my tank to catch a fish if it doesn't work out.