It's usually easy to get paint off wood, but when the wood has a finish, you have a problem: how to get the paint off while leaving the finish intact. Sanding is out of the question, and you can't use heat, so that leaves one option, which is to use a solvent that will remove the paint without damaging the underlying finish.
It may be easier than you expect to find a solvent to do the job, especially if the finish is a curing one, like varnish. Once varnish cures, it's impervious to all but the strongest solvents. The same can't be said of lacquer and shellac, however, which are finishes that dry but don't cure, but you'll be helped by the fact that solvents that can remove the paint probably won't affect them. In any case, it's always best to start with the weakest solvent and progress to stronger ones only if necessary.
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1. Use Soap and Water
Good old soap and water may do the trick. Mix a fairly strong soap solution by combining an ounce of dish soap and a cup of warm water. Soak a rag in the solution and start rubbing. You can also use something mildly abrasive, such as a kitchen scrubbie, but you need to use less pressure than you do when rubbing with a rag to avoid scratches. This method should soften the paint just enough for removal, and if not, try adding a little vinegar to the mixture for extra cutting power.
If you're just trying to remove a few spots of overspray, you might not even need a soap solution. Just scrape them off lightly using a plastic putty knife. Don't use a metal scraper, though, or you're almost certain to scratch the finish.
2. Use a Commercial Paint-Removal Product
If you don't have any luck with soap and water, try a commercial paint-removal product. Lift Off is one such product with a water-based formula that will soften water-based aerosol spray without damaging varnish, lacquer, or other hardened surface coatings. Just use it according to the directions on the container, which basically instruct you to spray it on and wipe it off with a rag along with the paint.
If the paint is fresh and hasn't completely dried yet, you may be able to remove it with olive oil. Spread the oil liberally on the paint and rub it off with a rag. You could also use motor oil for this, but olive oil is preferable because it doesn't have a strong odor. Mineral oil is another safe, low-odor oil you can use for this purpose.
3. Use a Stronger Solvent
Sometimes, you need a stronger solvent, but you want one that won't damage the finish underneath the paint. If the paint you're trying to remove is latex, the best choice is isopropyl alcohol but not if the underlying finish is shellac. Test the finish in an inconspicuous spot by rubbing on a little alcohol and noting whether or not the finish softens. If not, you're good to go, but if it does, the safest alternatives are paint thinner or mineral spirits.
Paint thinner or mineral spirits can remove most types of spray paint, even if they are oil-based, but they can dull the existing finish. If you have to resort to this method, you may have to polish the finish with wax after the paint is gone. Spread the wax on the dull areas and buff it up with a soft rag. You may want to wax the entire surface — not just the spots that were painted over — to restore a uniform sheen.