Any county of the state, through its board of county commissioners, may exchange tracts of land belonging to such county within any Indian reservation in said county, for lands of like character and value belonging to the United States government on Indian reservations within the state. The county may execute and deliver proper conveyances of such lands in the manner and form provided by law, but without the necessity of complying with any statute requiring notice of exchange or competitive bidding, and may accept in return therefor a proper instrument of conveyance to the county of the lands of the federal government for which such county lands are exchanged. Such lands exchanged by the county shall be appraised in the manner provided for the sale of real property acquired by the county for delinquent taxes, and the exchange shall be subject to the approval of the appropriate department of the federal government.