Ok, here's what you do: Get a copy of (a) the law requiring men to register and (b) the driver's license [or other official ID], and (c) a statement to the effect of "I, the undersigned, am female and therefore by [LAW CITE] not required to register for selective service" -- get this copy notarized and send it off.
If/when the bureaucrats rankle at having their authority challenged, grab a lawyer and prosecute them [the agency] corporately under Deprivation of Rights Under Color of Law & Conspiracy Against Rights — and individually under 42 USC § 1983 - Civil action for deprivation of rights.
The 18 USC series sections are applicable because they have clauses like exercise or enjoyment of any right or privilege secured to him by the Constitution or laws of the United States, or because of his having so exercised the same
and the very law that they would prosecute her under in inapplicable to her and to enforce it would then deny all jurisprudence and legislation.
Good idea!