I recommend you wash it on its own. If you have a washing machine with a hand wash cycle, it's your easiest and best choice. If you have an agitator in your machine, I recommend you put the skirt in a mesh bag/garment bag and use a COLD hand wash/ gentle cycle (if you have a front loader or no agitator, you don't need to put the skirt in a garment bag). Use a bit of shampoo (best soap for silk) and hang the skirt to dry in the shade. Once fully dried, you can iron directly on the skirt on a silk setting or even higher setting if you prefer.
Gently wash in a bucket or your tub with cold water and a few drops of any kind of shampoo (best soap for silk). Do not soak for more than 5 minutes, rinse, squeeze the water out, give a good shake and hang to dry in a shady place. Silk dries quickly and once fully dried, you can iron the skirt on a silk setting or even higher setting.