I collect silk cloth, but have trouble cutting it due to loss of function in my hands. I also quilt (or rather, collect quilt stuff and read about it a lot). There’s a thing called English Paper Piecing, where you cut fiddly shapes using wax paper as stabilizer. This helps prevent distortion of the cloth when being cut and handled.
For this experiment I used a piece of silk twill (not thick, but not organza, and a little thicker than your standard plain weave silk scarf). I sandwiched it between two pieces of wax paper from the grocery store.
Use a hand iron, no steam, on ‘silk’ setting, and press the sandwich for 10 seconds. I had a t-shirt below, and a handkerchief above, to absorb any errant wax.