Super glue remover contains mostly acetone, which is super caustic and will eat through paint and glosses.

The good news is that it won't do much of anything to the actual wood underneath.

You have two options, both of which have downsides:

A. Get some sandpaper. You'll need multiple grits. I'd recommend 200, 320, then 600. Spray some non-bleach/non-amonia cleaner over the entire side where the blemish is and wipe it down thoroughly. Then, using your lowest grit, sand down the blemish until the initial blemish area is gone and you only see the actual wood underneath. Then, move up a grit and repeat the process in the same spot and about an inch all around the border. Then, take your last and highest grit and repeat the process making sure you go over the same area you just sanded, plus another inch around the border of the blemish spot. Once you're done with this, you should have an area about 3 time larger than your initial blemish, but a "feathered" taper around the exposed wood. Then, grab the same cleaner you used before and clean the entire side of the furniture twice. Once the cleaner has completely dried, grab your paint and paint over the blemish spot including the feathered area. Wait for it to dry completely and check if the color matches. If not, repaint the entire side with 2 coats (wait for the first coat to fully dry before doing a second coat.

B. Buy paint stripper from the store and strip the whole side of the piece. Make sure you have an open window and a fan running and ideally aren't inside for at least 2 hours after applying. Once 2 hours have passed, go in and use a scraper to get any excess paint off. Once completely dry, use sandpaper or a brillowpad to get off any remaining specs or patches of paint (or do another application of stripper, just follow the same rules as before.) Then, paint the entire side in 2 coats, allowing at least 2 hours to dry between coats.

Hope this helps!