I'm pretty sure it doesn't really matter. I'd say try both wavy and straight hair in your headshots, then choose the picture you like best.
"You have two kinds of shows on Broadway – revivals and the same kind of musicals over and over again, all spectacles. You get your tickets for The Lion King a year in advance, and essentially a family... pass on to their children the idea that that's what the theater is – a spectacular musical you see once a year, a stage version of a movie. It has nothing to do with theater at all. It has to do with seeing what is familiar.... I don't think the theatre will die per se, but it's never going to be what it was.... It's a tourist attraction." Stephen Sondheim