Cold water hand washing is much better for silks than the dry cleaners. My structured silk, cotton and woolen clothing goes to a green dry cleaners--I don't notice any smell. I also cold water wash silk, cashmere and woolen knits.
I'm also sensitive to fragrances. Can't stand Dryel or the Woolite version. Airing the clothing out after cleaning doesn't seem to help that much.
I hate it when a simple cotton item (not a tailored jacket, for instance) is labeled Dry Clean Only. Unless it is a print with colors that might run (and why are manufacturers using these anyway?) I either wash the item or just let it stay in the store.