There is another reason for having the wig. In one comic situation where Lois used a computer to figure out what would happen if she had come from Krypton instead of Superman, she used a black wig to hide her black hair.
However, since Clark Kent did the "cut your hair to see if you are Kryptongirl" test, it actually helped to have a wig.
Fortuantly for Clark in L&C, Diana Stride never came up with an idea like trying to cut his hair, since as we saw in "Chip off the Old Clark" even a single strand of his hair can break scissors.
