I'd agree with Ginbottle - I've a few silk shirts that I wash on a "delicates" programme then hang out to drip dry. My mother doesn't even use clothes hangers for this, she threads an old pair of tights (pantyhose) through the sleeves and pegs the tights to the line.
If it needs ironing, try and do it when the shirt is still a little damp. Iron on the inside of the shirt
As for the washing liquid, there are a couple on the market suitable for machine washing of delicates but do unscrew the cap and smell them before you buy - one of the brands is very, very sweet and sickly smelling and lasts until you wash the shirt again...
Good luck!