If privately owned land is surrounded completely by areas designated by Part II of this subtitle as State wildland, the private owner and his successor in interest has the rights necessary to assure adequate access to the privately owned land, or the privately owned land may be exchanged for State-owned land in the same county of approximately equal value under authority available to the Secretary. However, the State may not transfer to a private owner any mineral interests unless the private owner relinquishes or causes to be relinquished to the State the mineral interest in the surrounded land. If valid mining claims or other valid occupancies are wholly within a designated wildlands area, the Secretary, by regulations consistent with the preservation of the area as State wildlands, may permit ingress and egress to the surrounded areas by means which have been or are being customarily enjoyed with respect to other areas similarly situated.