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I've worked with acetone at a few places where I've worked in the past. We used it to clean components for assembly, so I'm familiar with it. We always used it under a vent hood, but it evaporates pretty fast so I can probably safely work with it at home if I'm outdoors.
I've never actually bought it myself. Isn't nail-polish remover essentially acetone? Or, should I buy stuff labelled as such? Could I get it at the local pharmacy?
OK, I feel better talking about it on a more "adult" level.
You want to buy it at Home Depot/Lowes or a paint store - nail polish remover is essentially acetone but many use additives for color/scent/who knows what and they might not tell you what those additives are. I buy it by the quart - as if I'll ever need that much - but it preserves well because the manufacturer knows darn well it
wants to evaporate and provides a nice seal on the top.
Me, I use it in the bathroom, atop the throne, door closed and window open. I'm single, though - you may have other considerations.

Your biggest worry is a successful application which reveals surfaces which haven't aged as quickly as the rest, creating an obvious difference. This is an ongoing problem, but in your case I feel it's justified. Heck, a Details 1889-CC is still a sizable value.
Acetone is completely inert as regards silver, and will not interfere with any existing tarnishing process. In this case, I'd advise removing as much of the sticker as possible manually first. Heat would help. A toothpick or a rose thorn (my preferred tool) to help is incapable of scratching the silver. Use the acetone to remove only the adhesive, if you can. With this one, you're going to want to give it one hour in a jigger glass of acetone - ensuring it leans and does not lay flat (I cover mine with a pane of glass to inhibit evaporation), then rinse it under full-pressure tap water (the next dip will instantly remove the water) and repeat that process probably two more times, reducing the immersion duration each time. Rinse it
hard each time, and with luck your last momentary acetone dip will be for the specific purpose of removing the rinse water, which it will do. Last step is dropping (exaggeration) it onto a paper towel for the few second the acetone will take to evaporate. Acetone is a "final" rinse in that if it's pure enough, you need not touch the coin again with anything.
Should the adhesive prove to me more recalcitrant, immersions of 24 hours are not a problem. Just understand that it's quite possible for whatever is precipitated into the acetone to redeposit itself back on to the coin, lengthening the process.
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OK, since I'm an official representative of Coin Community, caveats are in order.
Do not drink this stuff. Do not dip a finger into it and snort the result. Do not wash your clothing in it, especially if your dryer uses gas. Do not wash your children nor your pets in it. Do not have a Satanic ritual, including candles, anywhere near it. Do not allow an open container of it to be in the same zip code as any open flame. Do not smoke on the same side of the Mississippi River as this stuff is located. Do not use it on Earth if any volcano on the planet is erupting.
And for God's sake, do not use it as bong water.