Advice about hand-washing dry clean only fabrics?

I have some scarfs which have been packed away since this time last year. They kind of smell. They’re all coincidently made of rayon and are dry-clean only. I’ll be damned if I’d rather not pay to have them dry-cleaned. I read that washing rayon can make it shrink.
Do you think there’s any way around dry-cleaning my scarves?

If I wash them by hand, I’ll be using Dr. Bronner’s soap.