I had that happen a couple of years back. I was more concerned with the smell but the drive back did really wrinkle the kilt. Anyway, I didn't do anything except hang it up on the shower curtain rod.
The wrinkles were there still when it dried but after wearing it for a while again, the wrinkles were gone.
Maybe it was the Ontario humidity, anyway I didn't have to fuss with it.

You've provided a good solution if it doesn't clear up or you need it as soon as it's dry.