Please don't. It's possible that it would be all right, but it's very likely to shrink.
You can wash plain (non-beaded) thin crepe 1930s dresses. That's how they used to clean them at the time. My mum told me about helping her much older sister to wash her dresses in the Thirties. They would wash them, and the dresses would shrink. Then they would take a section at time (ie, the skirt part, from the waistband to the hem, and then the bodice part, and then the sleeves one at a time) and, each one of them holding one end of the section, pull really hard. They did it until they heard one or two of the stitches break, and that 'crack' was the signal that the section was back to being the right size. When I started buying vintage, I always did this with my plain crepe 30s dresses, and it worked perfectly. Even more oddly, those cracked stitches never started unravelling and needing re-sewing.
I wouldn't do it with a beaded dress, though, and I wouldn't do it with crepe that was anything other than 30s, as I've no idea what would happen.
It's really tricky to find dry cleaners who are good at cleaning vintage clothes. I've had things de-natured (ie, returned to me no longer feeling nice, as if they had been sort of hardened and dried out), and I had one disaster when a dry cleaner shrank a beautiful 1960s wool crepe suit of my mum's. If you love the dress, be careful where you take it, OP. Good luck.