Would you believe I have washed them -very successfully!- in my washing machine? Years ago in another collectors' group, a lady from Canada gave step-by-step instructions on how she washed hers. Since, at the time, I had the exact same model of washing machine (an early Magtag Neptune front-loader) I decided to try it. Worked beautifully. I have not tried it with my new LG machine, but it should work just as well. Most machines made in the past 15 years or so have a "hand-wash" or a "silk" cycle that is more delicate than the old "delicate" cycles. I used that setting, cold water, and small amount of Ecover® delicate laundry wash for HE machines.
I tried it first on a vintage carré I was giving a friend of her 50th birthday. Not sure if that was brave or foolish...
If anyone wants to try it, I would suggest using a scarf you're not too attached to, just in case.