Simple: You use sew-in interfacing.
Not all interfacing requires an iron; a very wide range of sew-in options exist and can be used with satin to give the completed garment more structure. Do note that the purpose of interfacing is to provide structure, not to make fabric easier to handle.
If you're looking for a way to stiffen the fabric while working with it, but maintain the usual structure of satin in the completed garment, you can try using a washable glue or starch, or sewing/gluing a bit of wash-a-way embroidery stabilizer in place; these will be removed by washing the garment, leaving you with only satin.
You can also sandwich your seams between pieces of wash-a-way to help guide it through the machine without slipping, and using sewing clips instead of pins to hold your pieces together. Wash-a-way is very easily removed, and clips won't contribute to puckering or fraying while providing a greater area of contact with the fabric for stabilization.