If you quit hanging them to dry, you'll have an easier job of pressing.
I wash my SWKs on Cold water, Gentle cycle. After the wash, rinse and spin, I run it through an extra spin dry. I used to then take it after the spin and hang it up, with a bunch few clip style hangers. And no matter how much smoothing and plulling of pleats I did, I had a lumpy mess and an hour of ironing the next day.

I figured out that laying the kilts out to dry was the way to go. I put a sheet over our spare bed, and carefully spread the kilt out flat. Take some time to lay it out so it is as flat as possible and straighten and smooth out the pleats and aprons by hand. Spend 10 minutes doing that, and once it dries you should only need minimal ironing.

If you don't have a spare bed, a big table or even the floor will do. I do my pressing over a blanket on our seldom used dining table.