Can I, a white non-Muslim, wear a thawb to a Renaissance festival?

I'm going to a renaissance festival, and I've always been intrigued by the trading aspect of history. The Arab world has essentially always been the hub for commerce, and I'd like to dress as a trader from the medieval era. As most trade came from the Middle East, most traders dressed in traditional clothing, whether they were European, Chinese, Indian, African, or native to the region. In a modern context, but the context being a renaissance festival, wherein it is common to dress as though you're from the medieval ages, would it be culturally inappropriate/insensitive to wear a thawb (the easiest to purchase modern equivalent) to complete the outfit?