Dish soap works good too - no water .. well, maybe a TINY bit .. but it should slide right off. Another is lotion. Baby oil. Yup, been there done that ... actually just the other day! (My pregger fingers have now officially swollen to where I can wear my wedding rings now
I hope the ring is alright, Its a bummer I know.
(A side story of stuck-ness: When our first boy, Jake was oh about 7 months old, he had gotten his leg stuck in between the crib slats while sleeping. He woke up Howling mad and both me and hubby ran into the room. Sure enough, stuck tight. We both had a very minor first second freak out. Then, hubby runs out of the room yelling, "Hang On! Be right back!!" I stood there ... contemplated ... casually picked up some baby oil .. greased the tubby lil leg up and 'pop' .. out it came. Of corse, a minute later hubby runs into the room holding up a hammer and a saw.
It was like something out of a movie!!
I asked "What are you Doing?!" .. He looked at a just fine Jake and said, "Good thinking there hun." I could have died laughing!!