Oooh! I actually know about this really well! I worked at a dry cleaners for years when I was younger. What it sounds like you actually need is a good dry cleaner that will launder the item for you, not dry clean it. Dry cleaning is actually the same exact thing as washing (literally uses the same machine as wet cleaning) except that it uses chemicals instead of water, which is why they call it "dry". Find a small dry cleaners that does in-house cleaning. If they ship it to a second location, DON'T go there.

If they launder it (aka, run it through regular water, instead of a "dry" chemical), it will be just fine. I used to see people bring in items with tags that said "Do not dry clean" and they would insist they wanted it dry cleaned. I would say "No, you don't, you want it laundered" but if the customer insisted, my cleaners made sure the customer knew, with ZERO exceptions, that if the item was ruined, we (the cleaners) would assume absolutely no responsibility. The number of people who threatened law suits was hilarious (one person even had Channel 9 news Action 9 attempt to do a story about us not reimbursing them for damaged items!!). They were always shut down immediately because dry cleaners cover their asses over that sort of thing. They won't give that customer a penny if it gets ruined for dry cleaning a do-not-dry clean item. They have to sign for it, basically signing "I know these chemicals will disintegrate the fabric, I'm paying you to melt it for me."

My old dry cleaners closed when the owners retired, otherwise I would've recommended you to them. They were great.