I guess the specific question was about dry-clean only alternatives, but the source of the question was cat pee.

In my experience (and my cat has unfortunately supplied me with ample experience), the enzymatic cleaners that claim to remove cat pee odors are very good.  (Make sure to check with your local pet store to find a good one, though.)

I haven't tried vinegar, but I do know that washing with regular detergent is not a useful option (and I wouldn't be sure "wet cleaning" would be any different).  The odors remain, and the cat is tempted to use the same location again.  Whatever you use has to wipe out the odor, and enzymatic cleaners have done the trick for us.

Be sure to "spot test" the cleaner in an "out of the way place" on your item, to be sure it doesn't change colors or otherwise adversely affect your fabric.

And, as all the good cat veterinarian sites will point out, if your cat is peeing inappropriately, make sure to get the kitty checked out for possible urinary tract infections.

Dave