I would wash the silks first. (Shampoo is supposed to be good for washing silk. Google to find suggestions.)
Then I would experiment with both fusible nylon tricot and Misty Fuse. I found it cheaper to purchase fusible nylon tricot online from a drapery company; however, for test purposes you could use one of the packets that JoAnn's sells. I have found Misty Fuse available only online.
I personally think the Misty Fuse would be nicer, if it works, because it would keep the hand of the silk more true. Fusible nylon tricot is good, but it does add a lot of weight and some degree of stiffness.
For Misty Fuse, I would iron between sheets of Reynolds parchment paper.