Just adding my two cents. In both Supergirl and the imaginary stories involving a superpowered Lois (aka Krypton Girl, "The Superwoman of Metropolis" and "Lois Lane's Super Dream" mostly) both have her wearing wigs so it's not completely far-fetched that she (Claire/female Clark) would wear one. I do know that the Rule 63 cosplay of Superman just pulls her hair back a little in both versions and wears glasses as Clarissa Kent (Clark) but makes the Superwoman hair a little more poofy on top (source: Kit Quinn\'s Tumblr .)

Source info on a Superpowered Lois

CLARK: No. I'm just worried I'm a jinx.
JONATHAN: A jinx?
CLARK: Yeah. Let's face it, ever since she's known me, Lois's been kidnapped, frozen, pushed off buildings, almost stabbed, poisoned, buried alive and who knows what else, and it's all because of me.
-"Contact" (You're not her jinx, you're her blessing.)