I've ironed plenty a bridesmaid/formal dress and silk (at the last minute, darn those cramped closets!) The trick is those low settings on the iron (usually marked "silk") if you really afraid use a towel. If you're really cautious about ironing on silk then use a moist/damp cloth and iron on the cloth: instant steam. Even with a dry model iron you'll probably get most of the wrinkles out using a moist towel. Most hotels have an iron, towels, and water available, at least the ones I stay in do.

It's a myth that silk is a delicate... it's really a very sturdy fabric (except for chiffon silk), and you can iron it easily on a cotton setting too, as long as you don't let the iron sit. an easy way to iron is to puff steam on the fabric and smooth quickly.

Hang clothes on hanger.

Use an iron on high and high steam burst. Steam until fabric releases wrinkle(s), smooth by hand. Don't get the fabric wet, it will wrinkle again.

Have ironing board near by to rest the iron which becomes heavy in the vertical position.

Pack a bandana or hankerchief for a pressing cloth if ironing is needed.