About the only song with a wig in it I can think of off the top of my head (sic) is The Old Maid and the Burglar -

She took out her teeth and a big glass eye
And the hair off the top of her head...
I'm pretty sure that any song mentioning a wig would be likely to be poking fun at the wearer, male or female, I'm afraid. Unfair, but that's how it goes.

Dolly Parton makes no secret of the fact she wears a wig - I wonder if she's come up with any songs about it. (Funny when people go on about "singer-songwriters" they never seem to mention her...)