Most hotels in the U.S. now have ironing boards and steam irons. For sure you can rinse the kilt out it the tub and hang dry it over night and if you need/want to iron it in the morning. If it doesn't need actual washing you could let any wrinkles hang out over night or hang it in the bathroom while you shower to steam out the wrinkles or use the steam iron as a hand steamer on the hanging kilt.

Dry cleaning seems a bit of overkill, and then there's that funny smell...

Ron