Yes, in several different ways. Any time Cherokee people get married, it is a Cherokee wedding. The Cherokee Nation has a marriage law permitting tribal citizens to marry within the tribal government, without a state license. The marriage is recognized by all governments of the world. Contact the Cherokee Nation courthouse at 918-458-9440.
The people who are licensed to perform weddings under this law range from traditional Cherokee to many Christian denominations.
It is the belief system that makes the type of wedding, not the type of clothing. Decide if you want a Cherokee tribal wedding instead of a state license, or if you want a Cherokee traditional belief system wedding (there are traditional leaders who are licensed to do both weddings with state license or tribal license).