Although great care is taken on your silk underwear, once some clean has to be made, it appears that ironing is necessary, how to do it?
Silk has a resistance to creasing or wrinkling, most will smooth out naturally. If ironing should become necessary, press the damp silk cover on the reverse side with an iron set on low. Silk charmeuse (satin) requires a cool iron to bring back sheen. Be careful for your twin size silk sheets, anyway.