old RUMMY "GRAPEFRUIT DRINK" thermometer in need of help

This old thermometer was nailed to the outside of one of the old outbuildings on the farm for at least a couple decades back when Grandma and Grandpa still lived there and after -- no doubt he first put it there, apparently also deciding he didn't care to advertise RUMMY "GRAPEFRUIT DRINK", so painting over the "GET CHUMMY WITH RUMMY" ad slogan and graphic of their bottle/label on either end too, which can now again sort of be seen emerging thru the fading green paint layer. It is made of pressed steel, about 38" long and 8" wide. I haven't yet found mfr's markings or info (under the green?) but it still says "MADE IN U.S.A." under the temperature scale.

That outbuilding is long gone now, but I wasn't surprised in the least to come across the thermometer stowed away in Mom and Dad's garage. What was surprising (and very lucky for me?!) is that an original wooden strip on its backside which held the actual glass thermometer tube had been nearly *completely* eaten away by termites/etc (probably while it was nailed to the wall outside) leaving the tube itself precariously close to being snapped into pieces. Happily it remains intact though, and I now have it safely stowed away in a protective tube until I decide what exactly to do with the rest of the thermometer and/or make a replacement strip to hold it.

Ultimately I'd like to try to remove the extra ugly green paint, but I'm not really certain how to best go about that without also wrecking the original paint/design underneath it. Probably will try (carefully!) several different potential methods to see if anything might appear to work...if no success I might have to just resign myself to fixing the thermometer tube and putting it back out someplace in the sun (so's to fade further, quicker) and leaving it 'defaced'. SUGGESTIONS ARE WELCOMED, ifn's anybody has any experience fixing signs like this??