Subject to valid existing rights, each wilderness area designated by this subchapter shall be administered by the Secretary in accordance with the provisions of the Wilderness Act [
16 U.S.C.
1131 et seq.], except that any reference in such provisions to the effective date of the Wilderness Act shall be deemed to be a reference to December 21, 2000, and any reference to the Secretary of Agriculture shall be deemed to be a reference to the Secretary of the Interior.